Methods for determining wafer temperature

ABSTRACT

Methods and apparatus for wafer temperature measurement and calibration of temperature measurement devices may be based on determining the absorption of a layer in a semiconductor wafer. The absorption may be determined by directing light towards the wafer and measuring light reflected from the wafer from below the surface upon which the incident light impinges. Calibration wafers and measurement systems may be arranged and configured so that light reflected at predetermined angles to the wafer surface is measured and other light is not. Measurements may also be based on evaluating the degree of contrast in an image of a pattern in or on the wafer. Other measurements may utilize a determination of an optical path length within the wafer alongside a temperature determination based on reflected or transmitted light.

RELATED APPLICATIONS

The present application is a continuation application of U.S. patentapplication Ser. No. 11/478,312 which was filed on Jun. 29, 2006.

BACKGROUND INFORMATION

A thermal processing chamber as used herein refers to a device thatrapidly heats objects, such as semiconductor wafers. Such devicestypically include a substrate holder for holding one or moresemiconductor wafers or other objects and an energy source for heatingthe wafers, such as heating lamps and/or an electrical resistanceheater. During heat treatment, the semiconductor wafers are heated undercontrolled conditions according to a preset temperature regime.

Many semiconductor heating processes require a wafer to be heated tohigh temperatures so that various chemical and physical transformationscan take place as the wafer is fabricated into a device. During rapidthermal processing, for instance, semiconductor wafers are typicallyheated by an array of lights to temperatures from about 300° C. to about1,200° C., for times that are typically less than a few minutes. Duringthese processes, one main goal is to heat the wafers as uniformly aspossible.

During the rapid thermal processing of a semiconductor wafer, it isdesirable to monitor and control the wafer temperature. In particular,for all of the high temperature wafer processes of current andforeseeable interest, it is important that the true temperature of thewafer be determined with high accuracy, repeatability and speed. Theability to accurately measure the temperature of a wafer has a directpayoff in the quality and size of the manufactured integrated circuit.

One of the most significant challenges in wafer heating systems is theability to measure accurately the temperature of substrates during theheating process. In the past, various means and devices for measuringthe temperature of substrates in thermal processing chambers have beendeveloped. Such devices include, for instance, pyrometers, thermocouplesthat directly contact the substrate or that are placed adjacent to thesubstrate, and the use of laser interference.

In order to use pyrometers in a thermal processing chamber, thepyrometers generally need to be calibrated. Consequently, variouscalibration procedures currently exist to align the temperature readingsof the pyrometers with an absolute and accurate temperature reference.One widely used method to calibrate pyrometers in thermal processingchambers is to place in the chambers a semiconductor wafer having athermocouple embedded in the wafer. The temperature measurements takenfrom the thermocouple are compared with the temperature readingsreceived from the temperature measuring devices and any discrepancy iscalibrated out.

Although this method is well suited to calibrating temperature measuringdevice, such as pyrometers, it requires a substantial amount of time tocalibrate the instruments. As such, a need currently exists for a methodof calibrating pyrometers in thermal processing chambers very rapidlywithout creating a substantial amount of down time. In particular, aneed exists for a method of calibrating pyrometers in thermal processingchambers without having to open the chamber, in order to maintainchamber integrity and purity. A need also exists for a simple method forcalibrating pyrometers in thermal processing chambers that can be usedroutinely as a regular check to verify that the optical pyrometry systemis properly functioning.

Furthermore, a need exists for a method of measuring temperature andcalibrating pyrometers in thermal processing chambers that can be usedacross a range of temperatures, including for accurate high-temperaturemeasurement and/or calibration.

SUMMARY

A method of calibrating a temperature measurement device can includedirecting an incident ray of light towards a first side of a calibrationwafer, detecting light energy comprising at least one ray of light thathas traversed a path within the wafer and has been reflected at areflective plane, the reflective plane being distinct from the firstside of the calibration wafer, determining the absorption of the waferbased on the detected energy, determining the temperature of the waferbased on the absorption, and calibrating a temperature measurementdevice based on the determined temperature. For instance, the reflectiveplane may comprise an interface between two layers of the wafer, a layerbetween two layers of the wafer, a gap between two layers of the wafer,the second or back side of the wafer, and may comprise a pattern ordiffraction grating.

Detecting light energy can include detecting at least one ray of lightthat has exited the first side of the calibration wafer at apredetermined angle. The incident ray may be directed at an angle ofincidence and a plane-of-polarization selected to minimize the surfacereflectivity of the wafer.

The wafer may comprise an absorbing layer and a substrate, and theabsorbing layer and substrate may be selected from materials havingdiffering refractive indices at the wavelength of the incident ray oflight such that the reflective plane is disposed at the interface of theabsorbing layer and the substrate. Alternatively, the wafer can compriseat least one additional layer between the absorbing layer and thesubstrate, with the reflective plane defined at the additional layer.The absorbing layer and the substrate can both comprise silicon, withthe additional layer comprising silicon dioxide, although othermaterials are suitable for any of the layers.

The wafer can comprise a grating at the interface between the absorbinglayer and the substrate, with the grating defining the reflective plane.The detected light energy may then comprise light that has beendiffracted by the grating.

The first side of the wafer can comprise an anti-reflection coating, andthe wafer may also comprise a reflection enhancing layer or coating, thereflection enhancing layer defining the reflective plane.

The wafer may include a gap between the absorbing layer and substrate,the gap defining the reflective plane.

The wafer can also include a textured front side.

The wafer may be configured so that the reflective plane and a firstside of the wafer are inclined relative to one another. For instance,the absorbing layer may be constructed so that the first surface of theabsorbing layer is not parallel to the back surface, or the absorbinglayer may be positioned atop another layer having a tapered shape.

The directed light may be emitted using a narrowband source or abroadband source, or may alternatively comprise other electromagneticenergy.

One or more optical elements may be configured and arranged to direct aselected portion of the light energy reflected from the wafer into atleast one detector and/or selected portions of reflected light away fromthe detector.

The detector(s) may be positioned to detect light reflected from thereflective plane or light reflected at certain predetermined angles orranges of angles while not detecting light reflected from the first sideor at other predetermined angles or ranges of angles.

The wafer can include a pattern at the reflective plane, and determiningthe absorption of the wafer may include obtaining an image of thepattern and analyzing the image, such as by evaluating the degree ofcontrast in the pattern. The image of the observed pattern may beenhanced through use of a filter configured to block light reflectedfrom the first side of the wafer.

A calibration wafer suitable for use in calibration of an optical sensorcan include an absorbing layer configured to absorb at least a portionof light at a selected wavelength and a substrate. The substrate and theabsorbing layer can be selected and configured such that a reflectiveplane that reflects at least a portion of light at the selectedwavelength lies at a position distinct from the outer surface of theabsorbing layer.

The absorbing layer may comprise silicon, for instance. The wafer mayfurther include at least one additional layer between the absorbinglayer and the substrate. The substrate may also comprise silicon, andthe additional layer may comprise silicon dioxide. As noted above, thereflective plane and first or outer surface of the wafer may be inclinedrelative to one another. The first side of the wafer can include ananti-reflective coating, or may be textured. The reflective plane cancomprise, for example, a layer, film, or coating of reflection-enhancingmaterial, or may comprise a textured surface, a pattern, or a grating.Other suitable materials may be used in the wafer, such as, for example,Si, Ge, GaAs, InP, AlAs, GaN, InN, GaP, GaSb, InSb, SiC, diamond,AlGaAs, GaInAsP, InGaN, SiGe, or SiGeC.

A system for calibrating a temperature measurement device can include achamber, such an RTP chamber, adapted to receive a semiconductor wafer.The wafer may comprise a calibration wafer, and the chamber can alsoinclude a heating device in communication with the chamber andconfigured to heat the wafer. The system may utilize a temperaturemeasuring device configured to monitor the temperature of the wafer, andinclude a calibrating light source configured to emit energy comprisingat least one selected wavelength towards the wafer. At least one lightdetector may be positioned to detect the amount of light energy beingreflected from the wafer at the selected wavelength after the lightenergy has traversed a path, at least a portion of the path fallingwithin at least part of the body of the wafer.

The system may also include a controller in communication with the lightdetector and the temperature measuring device that is configured tocalibrate the temperature measurement device based on the detectedlight. The controller may comprise a computer system or systems, and mayalso control the other elements of the RTP chamber. The light detectormay comprise a photo or other optical sensor. The temperature measuringdevice can comprise a pyrometer.

A method of calibrating a temperature measurement device can comprisedetermining, for a first selected temperature range, the absolutetemperature of an object based upon measurement of the energytransmitted through the object from a calibration light source anddetermining, for a second selected temperature range, the absolutetemperature of the object based upon light reflected from the objectafter light has traversed a path comprising at least one reflectioninside the object. At least one temperature measurement device may becalibrated to account for variation from the absolute temperature in thefirst and second selected temperature ranges. The object may comprise acalibration wafer, and the measurement device may comprise a pyrometer.

The calibration process may be configured so that the upper limit forthe first selected temperature range and the lower limit for the secondtemperature range are approximately equal, and are defined by a fall-offin the transmitted light signal. The upper limit for the first selectedtemperature range and the lower limit for the second temperature rangecan both equal about 850° C. Alternatively, the first and secondtemperature ranges may at least partially overlap.

A method for determining the temperature of an object can includedirecting coherent energy towards an object such that the objectinteracts with the coherent energy. The interaction may include, forexample, transmitting or reflecting at least a portion of the energy.The method can further include directing incoherent energy towards theobject such that the object interacts with the incoherent energy. Anabsolute temperature of the object may be determined based uponmeasuring the incoherent energy after interaction with the object. Afirst measurement of the coherent energy after interaction with theobject may be performed, followed by a second measurement of thecoherent energy after interaction with the object, with the secondmeasurement being performed after the temperature of the object has beenchanged. Based on the first and second measurements of coherent energy,the change in an optical path length within the object may bedetermined, and the temperature change may then be determined based onthe change in the optical path length.

Determining the absolute temperature of the object may includedetermining the degree of absorption in the object based on measurementof incoherent energy reflected from the object and/or measurement ofincoherent energy transmitted through the object.

At least one of the coherent energy and the incoherent energy may bevaried in time, for example, by modulation.

The method may also include measuring the temperature of the objectusing a temperature measurement device and calibrating the temperaturemeasurement device based on the determined absolute temperature andtemperature change. The object may comprise a semiconductor processwafer or a calibration wafer, and the temperature measurement device maycomprise a pyrometer.

A method of determining the temperature of a semiconductor wafer caninclude providing an imaging system and using the imaging system toobtain an image of a pattern that lies in or on a surface of thesemiconductor wafer. The absolute temperature of the wafer may bedetermined based on the degree of contrast in the image. The pattern maybe viewed through a portion of the wafer containing a material withoptical properties that vary with temperature, with the portion lyingbetween the imaging system and the pattern.

The method may further include directing light energy towards thesemiconductor wafer, and the image of the pattern can be obtained bydetecting light from the source that has been reflected by the patternand/or transmitted through the wafer. Alternatively, the image of thepattern may be based on light emitted from the object. The determinedtemperature may be used to calibrate one or more measurement devices,such as a pyrometer.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure including the best mode of practicing theappended claims, directed to one of ordinary skill in the art, is setforth more particularly in the remainder of the specification, whichmakes reference to the appended figures, where like reference numeralsare intended to represent analogous features, and in which:

FIG. 1 illustrates an exemplary RTP chamber;

FIG. 2 shows an exemplary slab of material including a first and secondside, and illustrates multiple reflections arising in the slab when aray of energy A0 is incident on a surface of the slab;

FIG. 3 depicts generic examples of arrangements of layers in calibrationwafers;

FIG. 4 illustrates multiple reflections arising in an exemplarycalibration wafer;

FIG. 5 includes plots of reflectance measurements and simulatedreflectance measurements;

FIG. 6 illustrates an exemplary slab of material including a texturedsurface that may produce diffuse reflections;

FIG. 7 illustrates an exemplary slab of material and associatedreflections;

FIG. 8 illustrates an exemplary slab of material including at least onecoating or film and associated reflections;

FIG. 9 illustrates an exemplary slab of material including a gap;

FIG. 10 illustrates an exemplary slab of material and exemplary surfacetextures;

FIGS. 11 and 12 illustrate exemplary slabs of materials includingsurfaces inclined relative to one another and exemplary rays of light;

FIG. 13 illustrates an exemplary slab of material including a texturedsurface;

FIG. 14 depicts an exemplary embodiment of a slab configuration thatincludes a grating structure;

FIG. 15 shows an exemplary light focusing arrangement which may beconfigured to separate energy from selected reflections for detection;

FIGS. 16 and 17 illustrate an exemplary slab that includes a pattern andexemplary systems to image the pattern;

FIG. 18 shows an exemplary calibration wafer that includes selectedareas adapted for use in reflectance-based measurements;

FIG. 19 shows exemplary calibration wafer structural arrangements;

FIG. 20 illustrates an exemplary illumination and detection arrangement;

FIG. 21 illustrates an exemplary illumination and detection arrangement;and

FIGS. 22 and 23 comprise flowcharts including exemplary steps formethods of determining wafer temperatures.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments of thepresent subject matter, one or more examples of which are illustrated inthe accompanying drawings, with like numerals representing substantiallyidentical structural elements. Each example is provided by way ofexplanation, and not as a limitation. In fact, it will be apparent tothose skilled in the art that modifications and variations can be madewithout departing from the scope or spirit of the disclosure and claims.For instance, features illustrated or described as part of oneembodiment may be used on another embodiment to yield a still furtherembodiment. Thus, it is intended that the disclosure herein includesmodifications and variations as come within the scope of the appendedclaims and their equivalents.

U.S. patent application Ser. No. 10/178,950 by Paul J. Timans, filedJun. 24, 2002 and assigned to the present assignee, is herebyincorporated by reference for all purposes herein. U.S. patentapplication Ser. No. 10/178,950 describes various approaches fordeducing the temperature of a wafer including performing measurements oflight transmission through a wafer. Such measurements may find use indetermining the temperature of wafers undergoing a wafer manufacturingprocess. One particular application includes determining the wafertemperature and then using that temperature reading to calibrate apyrometer or other temperature sensor that is used to measure the wafertemperature. For calibration, a special wafer can be used whosestructure and composition is known ahead of the calibration procedure,so that its optical properties and their temperature dependence arepredictable. In this case, an in situ measurement of the opticalproperties can be used to deduce the wafer temperature. The opticalabsorption coefficient of the semiconductor substrate, α(λ,T), oftenexhibits a strong temperature dependence, hence measurement of α(λ,T)can lead to an accurate determination of the wafer temperature.

The optical transmittance, S*, depends on α(λ,T), and as a result,measurements of S* can be used to determine the wafer temperature. Also,the reflectance, R*, is also affected by α(λ,T), and hence it can alsobe used to monitor temperature.

A special problem of using transmission measurements to deduce the wafertemperature may arise for temperatures above ˜900° C. Difficulty mayarise for silicon wafers of typical thickness (e.g. 725 μm for 200 mmdiameter wafers or 775 μm for 300 mm diameter wafers), because at hightemperatures the optical absorption coefficient of silicon is quitehigh, and hence the amount of light transmitted by the wafer can becometoo small to measure accurately. Solutions for the problem may includeusing thin wafers, or wafers that include thin regions. The thin wafersor wafer regions are also made of silicon, but their thickness, d, ismuch smaller than that of the standard wafers (e.g. d<150 μm) so thatthere is a reasonable degree of light transmission at high temperature(e.g. >10⁻⁷) and accurate measurements can be performed, even attemperatures as high as 1100° C. One possible difficulty with thisapproach is that such thin sections or regions may be mechanicallyfragile, and hence making such wafers may be difficult and expensive.Another potential problem with the approach arises because differentregions of the wafer can be mechanically and optically different. Sincethe optical and thermal properties of the calibration wafer may not beuniform, the wafer may heat non-uniformly while being heated in the RTPtool, which could lead to more complex behavior during the calibrationprocess, and could potentially make results less accurate. Onealternative is to use a transparent substrate to support the thinsilicon wafer, or to use a wafer of a transparent substrate with asilicon surface coating of the desired thickness. However, suchstructures are generally expensive and complex to make. Furthermore,they may not resemble a typical wafer and hence might be less useful forcalibrating the pyrometer. Furthermore, the difference in thermalexpansion coefficient between the silicon surface layer and thetransparent substrate could cause stress in the substrate or in thefilm. Such stresses could cause damage and/or alter the opticalproperties of the silicon.

Because it can be difficult to use transmission measurements todetermine the temperature of a silicon wafer at high temperature,embodiments of the present subject matter provide ways to performanalogous types of temperature measurement based on the reflection oflight from a wafer. The approaches may be used in various ways todetermine the temperature of wafer. In particular, the approach allowsaccurate determination of temperature for the high temperatures wheretransmission measurements are difficult.

Various embodiments disclosed herein generally utilize a measurement ofreflected light to deduce the temperature of the wafer. The reflectedlight measurement can be performed within a semiconductor processingchamber, such as that shown in FIG. 1.

FIG. 1 illustrates an exemplary RTP process chamber 10 where the wafer12 is heated by banks of lamps 14 and 16. In the example shown the banksof lamps are both above (14) and below (16) the wafer. The wafer issupported within a process environment that is isolated from thesurroundings by windows both above (18) and below (20) the wafer 12.

One of skill in the art will recognize that chamber 10 is merelyexemplary, and the embodiments disclosed herein are equally usable inother types of chambers and chambers including configurations other thanwhat is shown in FIG. 1. For instance, although lamps are shown aboveand below the wafer, this is not necessarily the case in other chamberdesigns. Indeed, in other suitable chambers, the lamps may be replacedor supplemented by other heating sources, such as different lamparrangements, a susceptor, hot plate, or other contact-based heatingapproach, conductive heating, convective heating, RF or microwavesources, scanning lasers, and particle beams.

It should also be understood, however, that besides wafers, chamber 10may also be adapted to process optical parts, films, fibers, ribbons,and other substrates, and the use of the term “wafer” in the presentdisclosure is for example only, and is not meant to exclude any otherparticular shapes or substrates.

One of skill in the art will recognize that a variety of processes maybe carried out in chambers such as the one illustrated in FIG. 1 and forwhich accurate temperature measurements may be desired. For instance,the chamber may be configured and used for heat treatment or annealingof a substrate, during oxidation of the substrate, diffusion treatment,or during other processes which modify, add films, or otherwise involvea reaction of the surface and/or other part(s) of the substrate. Otherprocesses may include any suitable film deposition process, such as achemical vapor deposition process or an atomic layer deposition process.Still further processes may include plasma processing, ion implantation,ion implantation damage annealing, silicide formation, reflow,depositing a material on a substrate, or etching a substrate.

The windows may be made of quartz glass, sapphire, AlON, or any othermaterial that can transmit the energy from the lamps to the wafer. Thelamps are contained within a chamber that has walls 22. The walls mayreflect lamp radiation to improve the coupling of lamp energy to thewafer. Although energy is indicated as being projected through the samewindows as used by the various sensors to monitor emitted, reflected,and transmitted energy, chambers may be configured so that energy isprojected through windows separate from those through which the emitted,reflected, and transmitted energy is monitored. In fact, each suchsensor could have a separate window, and any window could be configuredto transmit or block certain ranges of energy in order to enhancemeasurement capabilities of the system.

The system also has various sensors and optical instruments that can beused to monitor the wafer during processing, as well as other equipment(not shown) to implement wafer processes, such as gas inlets/outlets,cooling systems, and the like.

FIG. 1 shows an exemplary configuration of instruments and sensors andan exemplary light source 30. Light source 30 is a source, orcombination of sources, that can illuminate the wafer surface byemitting a ray A0 that is incident on the wafer. The reflected light rayRA corresponds to an essentially specular reflection from the surface ofthe wafer. The reflected energy in ray RA can be detected by a sensor32. The reflected or scattered light ray RB corresponds to energy fromray A0 that is reflected in a non-specular direction. Such a ray canarise if the ray A0 encounters a surface in the wafer that is inclinedrelative to the surface that produces reflected ray RA. It can alsoarise from a scattering effect or a diffraction effect. The energy inray RB can be detected by a sensor 34. Some of the energy from A0 mayalso pass through the wafer, forming a transmitted ray T. The energy inthis ray can be detected by a sensor 36. Sensors can also monitor energyemitted by wafer 12 itself. For example, a hot wafer will emit thermalradiation. Sensor 38 can detect the radiation that is emitted from thetop surface of the wafer, E1. Sensor 40 can detect the radiation that isemitted from the bottom surface of the wafer, E2. The angle of incidenceof ray A0, and the angles at which the various sensors view the wafersurface can be selected as desired. Furthermore, the wavelength of theradiation emitted by source 30 can be selected as desired.

Source 30 may be a narrow band source, such as a laser, or a broadbandsource such as a lamp, an LED, a superluminescent LED, a super-continuumlight source or a hot object. In some applications it may even be an RFsource, a microwave source, or a THz radiation source, for example. Ingeneral it is a source of electromagnetic radiation, emitting radiationin the wavelength range between 100 nm and 1 m. The wavelength rangeemitted by source 30 can be selected or altered by the use of opticalfilters. When laser sources are used, the wavelength can be selected,for example, by choice of the type of laser, or by using a tunablelaser, or a multi-wavelength laser and by manipulating the laserwavelength through the use of non-linear optical media such as frequencydoublers and mixers. The state of polarization of the light emitted fromsource 30 can also be controlled. For laser sources, which often producepolarized light, this may involve controlling the orientation of thelaser and/or manipulating the orientation of the beam to obtain aparticular state of polarization with respect to incidence of the ray A0on the wafer surface. For all sources 30, the polarization may also becontrolled by the use of polarizing and/or retarding optical elements.The output of energy from source 30 may be continuous, pulsed ormodulated so that it varies with time. The state of polarization, theangle of incidence and the wavelength may also be modulated if desired.Although the radiation from source 30 is shown passing through thewindow, it may also be guided into the process environment by othermeans, such as light pipes, waveguides or optical fibers. In some casesthe radiation from source 30 might not be able to pass through thewindow material selected from transmission of lamp radiation. In thiscase a separate section of the window can be included, which is made ofa material that allows passage of the energy from source 30.

Filtering and polarizing elements can also be included in the optics infront of the sensors 32, 34, 36, 38, and 40. Such filters can be used todetermine the state of polarization and the wavelength range of theenergy that is detected in the rays that are reflected, scattered,transmitted or emitted by the wafer.

RTP chamber 10 and its components may be linked to a controller orcontrollers (not shown) for accumulating and processing measurementresults and controlling the light sources, heat sources, and othercomponents used in carrying out treatment processes. For example, thelight sensors and pyrometers may be linked to appropriate circuitryrunning algorithms to implement the various methods disclosed herein andperform various tasks such as, e.g., a computer system configured tocalculate wafer absorption based on light measured using the varioussensors as discussed below.

FIG. 2 shows how multiple reflections can arise in a slab of material 50when a ray of energy A0 is incident on at a first surface 52. Theincident ray is partially reflected at the first surface 52, producingray R1, but it is also partially transmitted producing an internal rayA1. Ray A1 is the reflected at a second surface of the slab 54, formingan internally reflected ray, A2. Some of the energy from ray A1 istransmitted through the second surface 54, forming a transmitted ray,T1. Some of the energy from ray A2 re-emerges from the first surface 52,forming a reflected ray R2, and so the process carries on. Because theintensity of reflected rays R2, R3, etc. are affected by absorptionwithin the slab, measurements of reflected light intensity are sensitiveto wafer temperature, and hence the approach described here can be usedfor temperature measurement. However, there are several significantchallenges in making such measurements very accurate, and these areresolved by the approach described here. The concepts described hereincan be used to assist in improving the accuracy of any measurement wherereflected light measurements are used to deduce the strength ofabsorption within a slab of material.

The slab 50 with first surface 52 and second surface 54 may correspondto a wafer or layer within a wafer or other object having a front andback surface. Depending upon the configuration of a particular system,for example, the front or upper surface may comprise the first surface52 and the back or lower surface may comprise the second surface 54, orvice versa. Therefore, the terms first and second surface are used toillustrate that the teachings contained in this document are equallyapplicable to objects in various orientations.

The skilled artisan will also recognize that the present disclosure usesvarious terms, including reflection, transmission, diffusion, andscattering. All such terms are meant to indicate interaction of energy,such as light energy, with an object or portion(s) of an object so thatafter such interaction(s), information about the object can be derivedbased on measuring the light (or other energy).

FIG. 3( a) shows a generic example of a calibration wafer 12 that can beused for calibrations, such as the high-temperature calibration problemdiscussed above. There is a surface layer 42 (also referred to as“absorbing layer 42” or “absorbing slab 42” herein) that absorbsradiation, the surface layer 42 positioned on top of a substrate 44. Theinterface between the surface layer 42 and the substrate 44 is such thatthe surface layer reflects at least some light. To achieve suchreflection, the optical properties of the substrate and the surfacelayer preferably are different. For example, the refractive indices ofthe surface layer and the substrate should be different at thewavelength that is being used for the measurement. However, if thesubstrate and the surface layer are the same, it is nonetheless possibleto meet this requirement by adding a layer between the surface layer andthe substrate. If the optical properties of this extra layer aredifferent to those of the surface layer and the substrate then it willreflect light and the requirement is met.

One example of how to implement the latter concept is shown in FIG. 3(b), where the wafer includes an additional layer 46 between layers 42and 44. In one embodiment, the wafer may comprise a silicon-on-insulator(SOI) wafer. The SOI wafer has a silicon substrate with two layerscoating its surface. The middle layer 46 on top of the substrate 44 inthis example is a layer of silicon dioxide. The top layer 42 is a layerof silicon. Such wafers are commercially available, from companies suchas SOITEC of Bernin, France. Such a wafer can be fabricated by bondingtwo silicon wafers together, where at least one of the wafers has alayer of silicon dioxide formed on its surface. After bonding, thethickness of either the surface silicon and/or the substrate silicon canbe decreased by any convenient means, such as polishing, etching oroxidation etc. Hence the thicknesses of the substrate, d_(sub), theoxide, d_(ox), or the surface layer of silicon, d_(si), can be chosen asdesired. The doping of these layers can also be set as desired. Forexample, the nature of the doping in the two wafers combined by thebonding process can be selected as desired.

By using the SOI structure, it is possible to form a relatively thinsilicon layer on top of a standard silicon wafer. Then, one can exploitthe effect of the temperature dependence of the absorption coefficientof silicon on the reflectance of such a structure to obtain accuratemeasurements of the temperature of the wafer. The skilled artisan willrecognize that other approaches may utilize SOI structures to measurewafer temperature. However, generally, in those cases, the temperaturedependence of the reflectance arose from the temperature dependence ofthe real part of the refractive index of silicon. As the refractiveindex varies with temperature, the optical thickness (refractiveindex×physical thickness) of silicon surface layer also changes. Theoptical thickness determines the nature of interference effects betweenlight reflected at the surface and that reflected at the oxide/siliconinterface. These interference effects result in oscillations betweenmaxima and minima in the reflectance as the temperature varies in thesilicon surface layer. Although this does provide an approach fortemperature measurement, there are some difficulties with that method.In particular, in order to make an absolute measurement of wafertemperature, it is necessary to know both the refractive index ofsilicon and the SOI film thickness with extremely high accuracy. Thisgenerally renders the approach impractical for determining the absolutetemperature with high accuracy. However, such methods can be used tomake accurate measurements of temperature changes, and they can becombined with embodiments of the methods of the subject matter presentlydisclosed herein for further benefits.

Although later discussion herein will generally make exemplary use ofSOI wafer structures, it should be recognized that there are manystructures that could be used to create calibration wafers by theapproaches described herein. For example, considering FIG. 3( a), thematerials that are used in the absorbing slab 42 and in the substrate 44can be chosen to best fit the application and the temperature range thatneeds to be calibrated. Likewise, the structure shown in FIG. 3( b) canbe modified by changing the materials of any or all of the three layers42, 44, and 46, or by replacing either or all of layers 42, 44, and 46with multiple layers. Changes in the materials can include changes inthe element or compounds used, changes in composition of alloys, changesin the phase or state of crystallinity and changes in doping or impurityconcentrations. A few examples will be considered here, but there arevery broad possibilities that will be apparent to one of skill in theart upon review of this disclosure.

One example may be the use of a structure such as that shown in FIG. 3(a), where the lower layer 44 is a heavily doped crystalline siliconsubstrate and the upper layer 42 is a layer of lightly doped siliconthat is grown epitaxially on the substrate. In this case, the change indoping will result in an interface that reflects infra-red radiation.Such a structure could be attractive because there would be an excellentmatch in the thermal properties of the two layers and hence problems ofthermal stresses during heating could be minimized. The doping in thesubstrate could be selected to be a rather slowly diffusing element,such as As, Sb or In, in order that the dopants do not diffuseexcessively into the undoped layer during the high temperaturecalibration process.

A three-layer structure analogous to that shown in FIG. 3( b) could alsobe formed by ion implanting dopants at high energy to form a buriedlayer that serves to generate the reflecting interface. Such a structurecould also be formed by ion-implanting dopants to form a highconcentration doped layer and then growing silicon epitaxially above thelayer. Another approach could include growing a heavily doped layer on alightly doped substrate, and then growing a lightly doped layer abovethe heavily doped layer. In all these cases the doped layer wouldprovide the difference in refractive index that generates reflected raysbeneath the silicon surface layer. Another approach would be to grow aSiGe alloy layer on a silicon substrate and then to grow a silicon layerabove the SiGe layer. As illustrated in FIG. 3( b), reference numeral 46would then represent a SiGe film. Once again, the advantage here wouldbe a closer match in the coefficient of thermal expansion. Structurescould also be created using polycrystalline or amorphous silicon,although such materials have less well characterized optical propertiesthan crystalline silicon has.

Such concepts also need not be confined to the use of silicon as theabsorbing slab 42 or as the substrate 44. In order to use the reflectionapproach to cover other temperature ranges it may be appropriate toselect other materials. For example, the absorbing slab 42 could containany semiconductor material, including Si, Ge, GaAs, InP, AlAs, GaN, InN,GaP, GaSb, InSb, SiC, diamond etc. It could also be a semiconductingalloy such as AlGaAs, GaInAsP, InGaN, SiGe, SiGeC etc. The compositionof such alloys could be optimized for particular applications. Theabsorbing layer 42 need not even be a semiconductor, provided it is amaterial whose optical properties vary with temperature. In particularits absorption coefficient at the measurement wavelength should varywith temperature. Likewise, the substrate 44 need not be silicon. Itcould be any of the materials mentioned above, or it could even be aninsulator or a metal.

In any such instances, of course, the skilled artisan will recognizethat the illustrated thicknesses such as d_(ox) and d_(si) wouldcorrespond to thicknesses of the actual materials used, with theappellations “ox” and “si” being used herein only for exemplarypurposes.

The disclosure will now discuss various embodiments of the presentsubject matter as implemented using an exemplary SOI wafer. However, inlight of the foregoing, it will be appreciated that the discussion of anSOI wafer is for purposes of example only, and use of other materials toimplement the disclosed structures, systems, and methods is entirelywithin the scope of the present subject matter.

FIG. 4 shows the paths of a ray of light, A0, incident on an exemplarySOI wafer 12 from an external light source. A fraction of the incidentradiation is reflected at the top surface, which has a reflectivityR_(tv) and transmissivity, T_(t). Another fraction passes through thesurface and forms ray A1, which reaches the interface between the oxidelayer 46 and the silicon film 42 and substrate 44. In this figure, theoxide layer is represented as a single plane that reflects some of theradiation incident on it. In reality there will be components of lightreflected at both interfaces of the oxide layer. For the currentdiscussion such effects will be included in the analysis by consideringtheir impact on the reflectivity of the lower surface of the siliconfilm, R_(ox). In general, radiation will also pass through the oxidefilm and be reflected and transmitted at the back surface of the wafer,however for the present discussion it will be assumed that the substrateis effectively opaque. Radiation reflected at the oxide layer can returnto the wafer surface 52 and exit, forming a second reflected ray, R2.The reflectivity of the surface for ray A2 is R_(ts). Since in generalray A0 can be incident on the wafer at any angle of incidence, θ₀, andin any state of polarization, the full analysis of the propagation ofthe rays requires all the reflectivities and transmissivities to takeaccount of the appropriate angle of incidence and polarization. This canbe done by performing separate analyses for rays incident with p- ors-polarization. Once properties for each of these cases have beenobtained, the corresponding result for any other state of polarizationcan be obtained by combining the results for p- and s- in an appropriatemanner.

From FIG. 4 it will be appreciated that the intensity of the reflectedray R1 is only affected by the reflectivity of the front surface of thewafer (WF), R_(tv), so that if the incident ray, A0, has intensity I,then ray R1 has intensity R_(tv)I. The ray that has been transmittedinto the substrate has intensity T_(t)I just at the point where it haspassed through the front surface region into the bulk of the wafer. Asthe ray A1 traverses the substrate it loses intensity because ofabsorption of energy. As a result it has an intensity aT_(t)I just atthe point where it reaches the oxide layer. The quantity a is theinternal transmittance of the silicon surface film, and is given bya=exp(−α(λ,T)d _(si)/cos θ_(i))  (Eq. 1)where θ_(i) is the internal angle of propagation. The latter angle isthe angle between the direction of the ray and the normal to the wafersurface. The portion of radiation that is reflected at the oxide layerto form ray A2 has intensity aT_(t)R_(ox)I just at the point where it isreflected. When the reflected ray A2 reaches the front surface it haslost more intensity as a result of absorption in the substrate and nowhas intensity a²T_(t)R_(ox)I. The portion of ray A2 that is reflected atthe front surface to form ray A3 initially has intensitya²T_(t)R_(bs)R_(ts)I, whereas the portion that is transmitted back outthrough the front surface forms ray R2, having an intensity a²T_(t)²R_(bs)I. The further propagation of ray A3 will generate more raysreflected and transmitted at the oxide layer, and the analysis of thepropagation of such rays follows in a similar manner. Summarizing thetotal energy reflected at the front surface of the wafer can beestimated from its reflectance R_(WF)*, given by

$\begin{matrix}{R_{WF}^{*} = {R_{tv} + {\frac{a^{2}T_{t}^{2}R_{ox}}{1 - {a^{2}R_{ts}R_{ox}}}.}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$This equation is adapted from the standard equation for light reflectedfrom a slab of material, which is given by

$\begin{matrix}{{R_{WF}^{*} = {R_{tv} + \frac{a^{2}T_{t}^{2}R_{bs}}{1 - {a^{2}R_{ts}R_{bs}}}}},} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$where the symbols have the same meanings as before, except that R_(bs)is the reflectivity of the back surface of the slab for radiationincident on it from within the slab. In deducing equation 2, R_(bs) isreplaced with R_(ox). Hence it will be recognized that the principlesdescribed here for improving measurement through the use of calibrationwafer based on an SOI structure will generally apply to any approachwhere the effects of absorption within a slab of material are exploitedin order to perform a measurement.

One of skill in the art will also note that expressions 2 and 3 wereobtained with the assumption that the intensities of the individual raysR1, R2, R3 etc. may be added together. This is a fair assumptionprovided that the reflectance is being estimated for light that can betreated as being incoherent. Light preferably can be treated as beingincoherent if the wavelength range of the light that is measured, Δλ, islarge enough compared to thickness of the silicon film. One criterion isthat

$\begin{matrix}{{{\Delta\lambda}\operatorname{>>}\frac{\lambda^{2}}{4n_{si}d_{si}}},} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$where n_(si) is the refractive index of the silicon film. For a siliconfilm that is 50 μm thick, considering the wavelength of 1.55 μm andassuming that n_(si) is ˜3.6, Eq. 4 indicates that Δλ needs to be muchgreater than 3 nm in order for the light to be treated as beingincoherent. For a thicker film, the requirement is less stringent. Forexample, for the same conditions but with a layer of silicon that is asthick as a standard for 300 mm diameter wafer, 775 μm, then Δλ needs tobe much greater than 0.2 nm. If the wavelength range of the light thatis collected at the detector is relatively small, then the light sourceneeds to be treated as being coherent. This means that the reflectancecannot be obtained by summing intensities of reflected beams, andinstead, the amplitudes of the electric and magnetic fields associatedwith each ray need to be summed in a vector fashion. Once this summationis performed, the intensity of the reflected light can be obtained fromthe Poynting vector as is customary in electromagnetic wave propagationanalysis. For coherent light, the propagation of the rays within thesubstrate needs to be considered with regard to both the amplitude andthe phase of the electromagnetic wave. The analysis can be performedusing the standard methods of thin film optics.

When an approach based on the reflection of light is used to deduceabsorption, the sensitivity of the method to absorption can be stronglyaffected by the relative magnitudes of the rays marked as R1 and R2 inFIGS. 2 and 4. Typical measurements of reflected light, such asreflectance measurements, collect energy from both these rays, andindeed may also collect energy from higher order reflections such as R3shown in FIG. 2, etc. One problem that can arise is when the intensityof the first reflected ray (R1), RtvI, is much greater than that of theother rays. In this case, the influence of the absorption within theslab on the detected light signal is reduced, relative to a case wherethe contribution of first reflected ray to the detected light signal issmaller that that from the other reflected rays, such as R2. The problemis illustrated through the results shown in FIG. 5.

FIG. 5( a) shows a theoretical prediction of the temperature dependenceof the reflectance of a slab of lightly doped silicon that is 775 μmthick at a wavelength of 1.55 μm. Because the absorption coefficient ofsilicon varies with temperature, the internal transmittance also changeswith temperature. This affects the intensity of radiation that emanatesfrom the wafer surface in rays such as R2 and R3 in FIG. 2. Thecalculation was performed for radiation incident on the wafer at normalincidence, and it was assumed that the back surface of the slab has acoating that made the reflectivity, R_(bs)=0.6. The reflectance of thefront surface was calculated for a front surface reflectivity,R_(tv)=R_(ts)=0.3 (plotted at 170 in the graph) or 0.0 (plotted at 174in the graph). The fraction of light in the R2 reflection was alsocalculated, for the case where the front surface reflectivity was 0.3(plotted at 172 in the graph). α(λ,T) for the wavelength of 1.55 μm wasobtained from the model given by Vandenabeele and Maex in J. Appl. Phys.72, 5867 (1992). The reflectance axis in FIGS. 5 (a) and (b) is shownwith a logarithmic scale, in order to emphasize the differences in thebehavior for the cases considered here.

At relatively low temperatures, <400° C., there is very littleabsorption in silicon at the wavelength of 1.55 μm, and as a result, thereflected light does not vary much with temperature. However as thetemperature rises above 500° C. the internal transmittance decreases andthe intensity of reflected light components such as R2 decreases, untilat temperatures >800° C., the wafer is effectively opaque and R2 etc. donot contribute to the reflectance. This trend explains the transition inthe reflectance (for the case shown at 170, where R_(tv)=R_(ts)=0.3)from ˜0.62 at ˜400° C. down to ˜0.3 at ˜670° C. However, it will beapparent that if the front surface reflectivity is reduced from 0.3 to0.0, a far more abrupt change in reflectance occurs, as it drops from˜0.55 at ˜400° C. down to <0.01 at ˜670° C. (as shown at 174). This isbecause if the front surface reflectivity is zero, then the onlyreflected light arises from the back surface reflection, and as thetemperature rises the latter tends towards zero. The same trend is seenin the curve for the component of the reflectance that arises from theray R2 (for the case where R_(tv)=R_(ts)=0.3, shown at 172) which dropsfrom ˜0.27 at ˜400° C. down to <0.01 at ˜650° C.

The effect of the differences in sensitivity to temperature change onerrors in temperature measurement can be seen in the results shown inFIG. 5( b). This figure includes three extra curves (171, 173, and 175)that represent examples that simulate measured temperature dependencesfor the quantities shown in FIG. 5( a). Each curve actually wascalculated from 90% of the values of the three curves shown in FIG. 5(a); the difference of 10% was introduced to simulate the effect of ameasurement error. It is then possible to deduce a “measured”temperature for any given reflectance measurement by comparison with thecorresponding theoretical curve. Examples are shown for a temperature of600° C. Here it can be seen that if the reflectance for a wafer with thefront surface reflectivity of 0.3 is measured, a 10% error inreflectance leads to a very large temperature error, ΔT₁, of ˜50° C., asindicated by curves 170 and 171. In contrast, measuring the reflectancefor a wafer with the front surface reflectivity of 0.0, a 10% error onlyleads to a temperature error, ΔT₂, of ˜6° C., indicated by the curves174 and 175. Likewise, in measurement of the reflected light componentR2 for a wafer with the front surface reflectivity of 0.3, a 10% erroronly leads to a temperature error, ΔT₃, of ˜6° C., as shown by curves172 and 173. These trends suggest that accurate temperatures can beobtained, provided that the amount of energy that 1R contributes to thereflectance is reduced, and/or if a component such as R2 is selectivelymeasured.

Embodiments discussed herein will aid in ensuring that the detectedlight signal is strongly affected by the absorption within the slab ofmaterial. It will be shown that by making the contribution of the firstreflected ray relatively small, it is possible to obtain a bettermeasurement of the absorption within the slab of material, and that thisapproach can lead to more accurate temperature measurement.

As noted above, the problem of the effect of front surface reflectionhas been discussed previously in literature. For example, Cullen et al.(IEEE Trans. Semiconductor Manufacturing 8, 346 (1995)) discussed thesuppression of the front surface reflection through the use of aBrewster angle incidence on silicon wafers. Cullen also contemplated thepossibility of applying an anti-reflection coating in order to suppressthe front surface reflection. The application was to study thetemperatures of metallized wafers, where a transmission basedtemperature measurement was hindered by the high degree of opacity ofthe front surface metallization. However, such approaches were limitedin temperature range by the thick wafer. They can also be relativelydifficult to use if the back surface of the wafer is rough, since thisleads to light scattering, which can affect both the absorption withinthe wafer and the effectiveness of the Brewster angle incidence approachfor suppressing the reflection.

Another approach that has been studied previously was diffuse reflectionspectroscopy (DRS). The principle of DRS is illustrated in FIG. 6.Generally, DRS can only be applied to wafers with a rough back surface.It relies on setting up a light detection system that does not collectlight reflected specularly at the smooth surface 52′ of the wafer 50′,but can collect light that passes through the front surface 52′ of thewafer and undergoes a diffuse reflection from the rough back surface 54′of the wafer. Some of the light that is scattered diffusely from theback surface can exit back through the front surface of the wafer andthen be collected by the light detection system. FIG. 6 shows how theinternal ray A1 is scattered at the rough back surface of the wafer,generating rays such as A2 a, A2 b, and A2 c. These rays can leave thesurface to form diffusely reflected rays such as R2 a and R2 b. Some ofthe scattered rays, such as ray A2 c, may be scattered through an anglethat is so large that when they reach the front of the slab, SF, theirangle of incidence exceeds that required for total internal reflection,and they cannot leave the wafer. A detector can collect light such asthat represented by rays R2 a or R2 b. These ravs leave the wafersurface at angles θ_(o2a) and θ_(o2b), which differ from that for thespecularly reflected rays such as R1, which is reflected at the angleθ_(o1), which equals the angle of incidence, θ_(o). By measuring thescattered light signal as a function of the wavelength of the incidentradiation, it is possible to collect a diffuse reflection spectrum. Theintensity of light that reaches the back surface and then isre-reflected and exits the front surface is strongly affected byabsorption of light within the substrate. Hence DRS is sensitive toabsorption within the wafer. A diffuse reflection spectrum collected bythis approach can provide valuable information about the relativestrength of optical absorption at different wavelengths, and hence itcan be used to determine wafer temperature. DRS has been implemented intemperature measurement products that are commercially available, e.g.the BandiT temperature monitor available from k-Space Associates, Inc.,Ann Arbor, Mich., USA.

Despite this, DRS does not address the main problem described in thecontext of the present subject matter, because the thickness of thewafer is generally too large for DRS to work for high temperaturemeasurements. Furthermore, there are some complications in using DRS,because the light scattering at the back surface is a complex effectthat depends on the nature of the surface texture there. This means thatdifferent types of back surface texture will lead to different signals,and the magnitude and angular distribution of the scattered radiation isdifficult to predict. Interpretation of such signals can be quitedifficult and hence in some cases it may be difficult to use theapproach to achieve an accurate measurement of the absorption in thesubstrate.

However, in accordance with embodiments of the present subject matterdisclosed herein, a number of approaches can be used to improve theaccuracy for sensing absorption within a slab of material by means ofmeasuring the reflection of light from the slab while avoiding thedifficulties that may be involved with approaches such as diffusereflection spectroscopy. The approaches will be illustrated by figuresusing the exemplary SOI structure discussed earlier, but as also notedearlier, they are also applicable to any type of slab of material. Forsimplicity, the full SOI structure is not shown in all the figures, butthe absorbing slab 42 is identified through the labels for its firstsurface 52, which the incident light first impinges on, and secondsurface 54, which lies at the other side of the absorbing slab 42. Asnoted above, in some embodiments, the first surface is the front surfaceof the slab and the second surface is the back surface of the slab, butthe arrangement may be reversed depending upon particularimplementations. In some presently-disclosed embodiments, the slab caninclude other features, such as surface coatings and textures asdiscussed further below.

FIG. 7 shows an exemplary configuration where the reflectivity of thefirst surface 52 is reduced by selecting an angle of incidence andplane-of-polarization for the incident radiation that minimizes thereflectivity of the front surface (R_(tv)) at the wavelength ofinterest. For example, the incident energy can be p-polarized, and theangle of incidence can be near the Brewster angle for the material ofthe surface. For a wavelength of 1.55 μm and a silicon surface, asuitable angle would be ˜75°. Since the front surface reflectivity isreduced by this approach, the relative contribution of rays such as R2is increased, and hence the reflected light signal is more sensitive toabsorption within the slab 50. Such an approach also has the addedbenefit that the front surface transmissivity, T_(t) is increased, andhence the magnitude of the intensity of P2 rises further. The skilledartisan will note that the same approach can be implemented by placing apolarizer in the reflected beam of light, rather than polarizing theincident light. In this case, the polarizer would be arranged so thatthe light detector only received radiation that corresponded to thep-polarization. The latter approach may have some advantages in somecases, for example it allows the amount of stray radiation that reachesthe detector to be reduced. Stray radiation could arise from the energythat is thermally emitted by the wafer or from radiation from theheating lamps. The approach could also be combined with the case wherethe incident radiation was p-polarized.

FIG. 8 shows a configuration where the reflectivity of the front surface52 is reduced by adding a coating 53 that reduces the reflectivity ofthe front surface. This anti-reflection (AR) coating reduces the frontsurface reflectivity, R_(tv) and the relative contribution of rays suchas R2 is increased, and hence the reflected light signal is moresensitive to absorption within the slab. Such an approach also has theadded benefit that the front surface transmissivity, T_(t) is increased,and hence the magnitude of the intensity of R2 rises further. The ARcoating should usually be a film that is highly transparent at thewavelength of interest, λ. Convenient films can include silicon oxide,silicon nitride, aluminium oxide, titanium, tantalum, hafnium orzirconium oxides. A “quarter wave” AR coating can be formed on thesurface of a material with refractive index n_(s) by forming a layer ofa material with a refractive index n_(AR)=(n₀n_(s))^(0.5) that ismλ/(4n_(AR)) thick to produce a reflectivity of almost zero forradiation incident from within a medium with refractive index n₀. Thequantity m is an odd-number integer. One example, for the case of anincident wavelength of 1.55 μm, would be to use a silicon nitride filmthat is 194 mm thick. Silicon nitride has a refractive index of 2, and afilm of this thickness provides a reasonable approximation to aquarter-wave anti-reflection coating. A silicon nitride film that is˜180 nm thick is effective over a reasonably broad wavelength range,e.g. for wavelengths between ˜1.1 and 2 μm. This is merely one exampleof an AR coating design, and more complex stacks of thin films can beused to similar effect. Indeed the performance of such coatings can beoptimized with respect to a range of wavelengths, angles of incidenceand planes of polarization for the incident radiation. Such designs canbe created with the aid of conventional thin-film coating designapproaches.

FIG. 8 also indicates an example of a configuration where thereflectivity of the back surface 54 of the slab is increased. Thisapproach is effective because it increases the amount of light reflectedat the lower surface of the slab of material, and hence it boosts theintensity of the ray R2, relative to that of R1. The reflectivity can beincreased by a number of approaches. For example a reflecting film 55can be formed at the back of the slab as shown in FIG. 8. The reflectingfilm may be a material with a high reflectivity, such as a metal, asilicide or other electrical conductor. It may also be a material with arefractive index that has a large difference to the refractive index ofthe slab of material. The refractive index may larger or smaller thanthat of the slab. In the case of the SOI film discussed above, therefractive index of the oxide layer is ˜1.46, whereas that for thesilicon film is ˜3.6, hence there is a large difference between the two.Other films could also be used, such as silicon nitride, siliconcarbide, aluminium oxide, a silicon germanium alloy, etc. A stack offilms could also be used to increase the back surface reflectivity. Thedesign can be optimized with the aid of conventional thin-film coatingdesign approaches. One simple example can be through optimization of theSOI structure itself. In this case, the thickness of the oxide layer canbe selected to make the reflectivity as large as possible. A largedifference in refractive index could also be obtained by having a gapbetween the silicon layer and silicon substrate beneath, because anygaseous material (or a vacuum) that fills this gap has a refractiveindex close to unity.

FIG. 9 shows a schematic diagram of such a configuration. In thisexample, the silicon surface layer 42 is held apart from the substratebeneath it by “support” regions 56 that determine the thickness d_(gap)of the gap 57. Such structures can also function to keep the surfacelayer of silicon attached to the substrate. The support regions could bemade of silicon or another material. One advantage of the structureshown in FIG. 9 is that the effects of different tendencies in thermalexpansion in the layers can be minimized. In any structure that containsfilms of different materials, the differences in the coefficients ofthermal expansion can lead to thermal stress as the object heats andcools. Such thermal stresses may deform the structure or alter itsoptical properties and are undesirable. By using the structure with thegap, as shown in FIG. 9, the effect of thermal expansion differences canbe greatly minimized. The support regions may be formed as an array ofpillars, and these pillars are free to move with the thermal expansionof the wafer. Hence thermal stresses are minimized. The pillars couldeven be made of silicon, in which case all the materials in thestructure can expand together in unison and thermal stress can becompletely eliminated.

FIG. 10( a) shows an example where the front surface reflectivity isreduced, but in this case the reflectivity is reduced by forming asurface texture 58 on Lie front surface 52. This texture can function inseveral ways. In one case, the surface texture can have the same effectas an anti-reflection coating. For example, the texture can lead to aregion near the surface where the effective optical properties are amixture of those of the incident medium and those of the slab ofmaterial. The texture can be in various forms, such as an array ofprotrusions 58′ from the surface (FIG. 10( b)), or grooves 58″ in thesurface (FIG. 10( c)). The grooves can be filled with a second material.The array can be regular (i.e. a repeated pattern with a pitch L_(p), asshown) or random in nature. The array can be one-dimensional, such as anarray of elongated grooves or fins, or two-dimensional, such as an arrayof pits or pillars. The degree of reflection of the surface can also bereduced by ensuring that the optical properties of the surface regionundergo a relatively smooth transition from those of the incident mediumto those of the slab of material. This can be done by making the surfacetexture take a form where the volume fraction of the slab materialgradually increases as the incident radiation traverses the surfaceregion into the slab of material. For example, FIG. 10( d) shows across-section through array of triangular fins 58′″ that achieve thiseffect. Conical or pyramid-shaped protrusions could produce a similareffect. One of skill in the art will appreciate that such concepts of“graded refractive index” can also be useful for reducing the surfacereflectivity when deploying a thin-film coating approach. In order toprevent excessive diffuse reflection from textured surfaces, the lengthscale of the lateral features of the patterns (e.g. the width of groovesor protrusions) can be made small compared to the wavelength ofinterest. The pitch of the pattern, L_(p), can be also be smaller thanthe wavelength of the light used in the measurements.

FIG. 11 shows an example of a case where the first surface 52 and secondsurface 54 of the slab 42 are generally not parallel, but instead areinclined relative to one another. In the example shown, the angle θ_(sb)between the back surface 54 of the slab and the directions normal to thefirst surface 52, e.g. N1 and N2, is greater than 90°. In this case, thedirections of the reflected rays R1 and R2 cease to be exactly parallel,and they take on different angles to the normal. Ray R1 is reflected atangle θ_(o1), which equals the angle of incidence θ_(o). Ray R2 leavesthe substrate at a different angle θ_(o2), because its internal angle ofincidence on first surface 52 has been altered by the reflection fromthe inclined back surface 54. This allows an optical system to separatethe energy in ray R2 from that in R1. The separation can be by means ofthe simple approach shown in FIG. 1, and in this case ray RA of FIG. 1would correspond to R1 in FIG. 11, while ray RB of FIG. 1 wouldcorrespond to R2 in FIG. 11. Hence the detector 34 would interceptenergy from ray R2 but not from R1. There is also the useful aspect thatit is also possible to collect the specularly reflected component R1.This signal can serve to provide a reference signal that can be used tocorrect for any variation in the light source characteristics. Manyother methods of separating the rays are possible once the beams R1 andR2 are not exactly parallel. For example, a lens can be used to bringthe light that is reflected at the front surface to focus at a differentlocation to that reflected from the bottom surface and a detector can beplaced at the position where the energy predominantly arises from areflection at the second surface 54.

FIG. 12( a) shows a case analogous to FIG. 11, except that in this casethe first surface 52 has been arranged to be inclined at an angleθ_(sf), so that is not parallel to the second surface 54 of the slab 42.Although FIGS. 11 and 12( a) have shown the sloping surface as being oneof the slab's surfaces, it is also possible to generate a reflected beamat an angle different to that of R1 by placing a sloping reflectingsurface beneath the slab. This may be simpler in some cases, for exampleif it is difficult to fabricate the slab with a sloping surface. Forexample in FIG. 12( b), for the example of an SOI wafer, the silicondioxide layer 46 can be tapered in thickness, making it wedge shaped. Inthe example shown, the interface between the SOI layer and the substrateis inclined at the angle θ_(ox) to the normal. The presence of areflecting interface that is inclined relative to the surfaces of theslab means that when the transmitted ray TX is reflected, it generates areflected beam, AX. Ray AX becomes an internal ray AB when it enters theslab 42. Since Ray AB is no longer parallel to internal rays such as A2,when it emerges from the front surface of the wafer as a reflected rayRB, its direction is not parallel to R1 or R2, and it leaves the surfaceat an angle θ_(ob). Hence it can be separated from the specularlyreflected components such as R1 and R2. Since the ray RB results fromrays that have traversed the absorbing slab, by monitoring itsintensity, it is possible to deduce the strength of absorption in theslab.

Although the examples given here have shown sloping surfaces that arestraight, these surfaces could be curved. Furthermore they could act asoptical elements that focus the beam of radiation that passes throughthe slab. For example the curved surface at the back of the slab couldform a curved mirror or lens structure that results in radiation fromrays such as A1 being focused. Since only the radiation that passedthrough the slab undergoes such focusing action, the beam that emergesfrom the surface of the wafer can be distinguished from that formed byrays such as R1, which merely undergo specular reflection at SF. Indeedthe back surface of the slab, or a region below it could be altered toform a variety of optical elements that change the direction of rayssuch as A2 and hence that of rays such as R2. Such optical elements caninclude lenses, curved mirrors, lens arrays, prisms and retroreflectors.It will be appreciated that, in embodiments of the present subjectmatter, the radiation may be reflected by an element entirely separatefrom the slab, such as a sloping mirror (or other element) positionedsuch that the slab is between the incident ray of light and the mirror(or other element).

FIG. 13 shows an exemplary configuration where the light reflected fromthe second surface 54 of the slab 42 is scattered into directions thatare not parallel to the specular reflection at the front 52 of the slab.This case is in some ways analogous to that used in the DRS approachdescribed above and shown in FIG. 6. However, in embodiments of thesubject matter disclosed herein, it is ensured that the film of materialin the slab is thin enough to allow a reasonable fraction of theradiation reflected at the second surface 54 of the slab to exit thefront surface 52 of the wafer even when the wafer is at hightemperature. The radiation is detected by a detector positioned so thatit can collect light that is reflected from the back surface of theslab, but not from the front surface of the slab. The configurationshown in FIG. 1 can be used, with the sensor 34 being used as a sensorfor light that is scattered, rather than specularly reflected. Thescattering at the back of the slab can be introduced by introducing atextured interface 62 as shown in FIG. 13. The texture can be formed inthe back of the slab, or in a structure below the slab. The mainrequirement in this configuration is that there is a feature presentthat leads to light being scattered at an angle, θ_(s) that is not equalto the internal angle of incidence θ_(i). Such light, represented by rayA2 in FIG. 13, will then emerge from the front surface of the slab in adirection θ_(o2) which differs from that of the specularly reflectedbeam, R1, which leaves the surface at angle θ_(o1)=θ_(o). The reflectedbeams R1 and R2 can then be separated by conventional means as discussedabove. There can also be benefits in applying a surface texture at thefront surface of the wafer. However this can lead to a more complexsituation where the rays incident on the back surface may have beenscattered at the front surface, and then may be scattered again as theyemerge through the textured front surface. Nevertheless, the net resultof using this configuration can be that the pattern of scattering (e.g.the angular distribution of the rays scattered) is different for therays reflected at the front surface to that for rays reflected at theback surface. As a result it may be possible to distinguish energy fromthe two reflections.

FIG. 14( a) shows a configuration where a grating structure 64 is formedat the second surface 54 of the slab 42. In this case the grating ispreferably designed so that it generates at least one ray of reflectedradiation that leaves the front surface of the slab in a differentdirection to that of the specularly reflected beam. This approach isattractive because it allows a predictable direction for the ray R2 thatis to be separated from the front surface reflection. The direction ofR2 can be controlled through the design of the grating, in particular bycontrolling the pitch of the grating. For example, the angles at whichthe ray A2 is diffracted, θ_(d), from an array with a period (pitch) ofL_(G) for a beam of light, A1, incident on the array in a medium withrefractive index n_(s) at an angle θ_(i) can be predicted from therelationshipn _(s) L _(g)(sin θ_(d)−sin θ_(i))=pλ,  (Eq. 5)where p is an integer describing the order of the diffracted beam. Manystyles of grating are possible, including arrays of lines, fins andgrooves of various shapes. A regular, periodic array of lines is justone example of how a grating can be formed. Periodic arrays oftwo-dimensional shapes, such as rectangles, polygons or discs, can alsoform the grating. The features of these arrays can be close to planar,such as a pattern formed by patterning a thin film of a material, orthey can have a three-dimensional aspect, such as an array of trenches,grooves, cylinders, parallelepipeds, spheres, hemispheres, ellipsoids,cones or pyramids. A grating structure can also be formed from an arrayof concentric circles. The essential feature of all these embodiments isthat they can generate a beam of diffracted radiation. The feature thatgenerates this beam can be at the back of the slab, or it can be at alocation below the slab.

In certain embodiments of the present subject matter, the array ofsupport structures shown in FIG. 9 could be used to form the gratingstructure. Any of the features discussed here can also have an aspectthat enhances the efficiency of the diffraction of radiation in thedesired direction. For example, they can exhibit a blaze angle in anapproach that is analogous to the use of blaze angles in a diffractiongrating. FIG. 14( b) illustrates the concept of using a blaze angle. Inthis example, the blaze angle is applied to the surfaces of the array ofparallel grooves. For the case shown a beam A1 is incident on the blazedgrating at normal incidence to the plane of the grating. The blazeangle, θ_(B) is set to maximize the efficiency of the reflection in thedirection of a diffraction angle of the grating, θ_(d), as definedthrough equation 5, e.g. by making θ_(B)=θ_(d)/2. Such concepts ofgratings can be combined with approaches that increase the reflectivityof the surfaces. For example, the reflectivity of elements of thegrating can be increased by using high reflectivity materials or byapplying thin film coatings. The use of gratings also opens the usefulopportunity of generating more than one diffracted beam and hencecollecting rays reflected at more than one angle from the wafer. Indeed,rays propagating in several different directions could be measured.Since these rays will all have experienced different paths through theslab, extra information can be obtained about the nature of theabsorption in the slab. Grating structures can also be applied to thefront surface of the wafer in order to optimize the approach.

Furthermore, the grating can also be used to separate wavelengths in anincident beam of light containing more than one wavelength. In suchembodiments, several beams like R2 can be generated by diffraction atthe grating, with each beam emerging from the wafer with a differentvalue of η_(o2). Several detectors (or an array detector) can then bearranged so that they each receive a different wavelength component andmeasure its intensity. This would greatly facilitate multi-wavelengthmeasurements, and since each wavelength can be guided to a differentdetector the filtering in front of the detectors could be simplified.This method would allow rapid evaluation of the absorption spectrum ofthe absorbing slab, in contrast to methods where either the sourcewavelength is scanned through a sequence of wavelengths and/or where awavelength selective element is tuned to allow the detector tosequentially sample the intensity at different wavelengths. This can bean important advantage for a scheme where a diffraction grating isdeployed at the back of the absorbing layer. It can also showsignificant benefits relative to a scheme such as the DRS method, wherethe scattering of different wavelengths happens in a manner that isessentially independent of the wavelength. In DRS, the detector thatsamples the scattered light is generally exposed to all the wavelengthsunless the light is specially filtered. In order to obtain an absorptionspectrum with the DRS method the reflected light has to pass through awavelength filtering element or a wavelength dispersive element such asa grating, a tunable filter or a prism.

FIG. 15 shows an example where the separation of energy reflected fromthe first surface 52 from that reflected from the second surface 54 isachieved through the use of a light focusing arrangement. An opticalsystem, which may comprise, for example, optical components such as theillustrated lenses and mirrors, is used to separate components ofradiation reflected at the two interfaces of the slab of silicon. Thefigure shows how two rays, A and B, emitted from a source of light Spropagate through the optical system. They are collimated by a lens L1,and then focused by a lens L2. The focal length and position of L2 areset so that an image of the source S is formed at the back surface ofthe slab, SB. The rays A and B form rays that are reflected at the frontsurface of the slab, RFA and RFB. They also form rays that are reflectedat the back surface of the slab, RBA and RBB. All of these rays passback through lens L2, are reflected by a beam-spitting mirror M and thenare collected by a lens L3. The lens L3 brings rays RBA and RBB to focusat a detector. Hence an image of the source S is formed on the detector,after reflection from the back surface of the wafer. In contrast, therays RFA and RFB are not in focus at the detector. Hence the signal fromthe detector is strongly affected by the reflection in the back surfaceof the slab. By measuring the component of light that is reflected atthe back surface it is possible to deduce the degree of absorption inthe slab.

FIG. 16 shows an example of a configuration that has some similaritieswith those in FIG. 14( a) and FIG. 15 above. However, in theseembodiments, a pattern 66 is formed at the second surface 54 of the slab42 and an imaging system 70 is used to image the pattern onto a detector72. In this case, the degree of absorption in the slab is assessed byobserving the degree of contrast observed in an image of the pattern 66that is formed using the optical imaging system 70. The imaging system70 will, of course, be connected to further apparatus (not shown) suchas, e.g., a computer and/or a display to provide an operator with a viewof the image; the computer may be configured to evaluate the degree ofcontrast in the image and provide other analysis functions. The contrastin the image describes the amount of variation of light intensityobserved in the image plane. As the temperature of the wafer rises, andthe slab becomes more absorbing, the magnitude of the contrast in theimage of the pattern diminishes, until the slab is effectively opaqueand the pattern can no longer be observed. A measurement of contrast inan image is attractive, since it automatically corrects for variationsin the characteristics of the light source illuminating the wafer. Suchan approach may also be able to improve the sensitivity for detection.

FIG. 17 shows one example of a method for improving the ability tomeasure the contrast in the image. In this case, the wafer isilluminated with radiation at the wavelength of interest, and thereflected light is imaged with a lens 68 in order to form an image at animage plane 71. As in the case of FIG. 16, the image can be analyzed byan imaging device 72, such as a camera, or by an array ofphotodetectors, or by scanning it over a single photodetector. As thetemperature rises, the contrast observed decreases and the temperaturecan be sensed by quantifying the relationship between the loss ofcontrast and the temperature of the wafer.

One practical problem with such an approach could be that a large amountof light that is reflected at the front surface of the wafer will alsoenter the optical imaging system. Although this light is not brought tofocus at the image plane, it contributes a background “stray light”signal that may decrease the contrast observed in the image plane andhence make measurements more difficult. One approach for reducing thisproblem is to insert a spatial filter 74 in the optical path between thepattern 66 and the imaging device 72. For example, this filter can beinserted at the focal plane 75 of the imaging lens 68, as shown in FIG.17. The distribution of light in the focal plane depends on the spatialfrequencies that characterize the pattern being imaged. The spatialfrequency describes the various length scales in the pattern. Forexample the pitch of a grating pattern represents one significantspatial frequency. The lengths of elements and spaces within a patternmay introduce other spatial frequencies. The light that is reflected bythe front surface of the wafer has a very low spatial frequency, sincethere is no pattern present there, and in effect it represents a “dc”background. The approach of using a spatial filter can eliminate thisbackground signal, leaving higher spatial frequencies. One way of doingthis is to place an opaque blocking element 76 on the central axis ofthe lens, in its focal plane, as shown in FIG. 17. If a grating is usedas the pattern then a suitable spatial filtering approach can involveplacing a mask in the focal plane of the lens, which selectively blocksspatial frequencies other than that corresponding to the pitch of thegrating pattern. The advantages of these spatial filtering techniquesare that they prevent large amounts of background light from reachingthe detector in the image plane. The background light contributes noinformation about the absorption in the slab, yet it can contributenoise to the signals being measured. It also greatly decreases thecontrast in the image and limits the range of signals that can beanalyzed by the detection system. Hence preventing background light fromreaching the detector may be very helpful in improving accuracy.

The method of using the degree of contrast in an image to characterizewafer temperature can be applied for various approaches. For example,the contrast may be observed in a reflected light signal or atransmitted light signal. It may also be observed in an emitted lightsignal. The latter approach has an added advantage that no externallight source is needed, simplifying the apparatus. Nevertheless, incertain cases the measurement may be easier to perform at the desiredtemperature if an external light source is used, because the magnitudeof thermally emitted radiation is very strongly dependent on the wafertemperature. This approach could be used for temperature measurement onpatterned wafers.

For example, the patterns on the front of the wafer could be viewedthrough the wafer thickness by observing them with an imaging systemthat looks at the back of the wafer. In this case, the degree ofcontrast observed in an image of a region of the wafer can be used asthe temperature indicator. This has the advantage of not requiring thewafer to be specially patterned, since the devices being processedprovide the necessary contrast themselves. Such an approach may also beapplicable in situations where the wafer is rotating. In this case thefluctuations associated with rotation of the pattern as observed by animaging system could themselves be used as a temperature indicator. Asthe wafer warms up, the degree of fluctuation observed by the imagingsystem reduces, because less light comes back to the imaging system fromreflections at the device side of the wafer. By selecting signals thatvary with time at the rotation frequency, it is possible to improve thesensitivity of such a detection system to the effect of the rotatingpattern. Such filtering can be achieved by a band-pass filter whose passband is centered on the wafer rotation frequency. The method can becombined with an optical approach of spatial filtering, in order todiscriminate against light that is reflected at surfaces other than thepatterned device regions.

In some embodiments, the observed patterns may be on the front side ofthe wafer and viewed through the wafer thickness, or may lie within thewafer, with the degree of contrast largely a function of the changingabsorption of material lying between the pattern and the imaging system.In alternative embodiments, the material forming all or part of thepattern may be sensitive to temperature changes. For example, all orpart of the material forming the pattern may become more or lesstransparent as temperature changes, change in refractive index, changein light scattering effect, vary in reflectance, absorptance, emittance,transmittance etc. Furthermore, for example, patterns may be devised toexhibit different combinations of the temperature-dependent changes.

Another method for distinguishing light reflected at the front of theslab from that reflected at the back is to illuminate the wafer surfacewith a pulse of light and to detect the times when reflected pulses oflight arrive at a detector. The fraction of the pulse that travelsthrough the surface of the slab and is reflected at the back surfacewill arrive at the reflected light detector a finite time after thefraction of the pulse that is reflected at the surface of the wafer.Such a measurement is quite challenging, because the time for light topropagate through the slab is relatively short. The speed of light insilicon is c/n_(si), where c is the speed of light in a vacuum andn_(si) is the refractive index of silicon, which is ˜3.6 at 1.55 μmwavelength, so the speed of light in silicon is ˜8.3×10⁷ m/s. Hence fora slab of silicon that is 100 μm thick, the time to travel through thethickness and back to the front surface of the slab is ˜200×10⁻⁶/8.3×10⁷s=˜2.4 ps. Although this is a very short time, in principle, the use ofshort pulse of light should enable measurements to discriminate betweenthe locations where the light is reflected.

The configurations described above can be used in combination in orderto get the most accurate temperature readings. For example, a wafer canhave an anti-reflection coated front surface with a highly reflectinggrating at the back surface of the slab. The wafer can be illuminatedwith p-polarized radiation, incident on the front surface at Brewster'sangle for the particular wavelength used in the measurement. The lightthat is diffracted by the grating at the back surface can be collectedby a detector that is configured and/or positioned so as to not collectspecularly reflected light.

For many applications the SOI wafer structure will be suitable for hightemperature calibration. Typically a wavelength of ˜1.55 μm can be usedfor the measurements, since silicon exhibits relatively low absorptionat this wavelength, and hence silicon films that are not too thin can beused in the SOI layer. The reflection approach generally utilizes sensedradiation that has passed through the film thickness twice (or more), soit is desirable for the absorption to be relatively low, as compared tothe situation that applies in a transmission measurement, where themeasured radiation need only pass through the slab thickness once.Although wavelengths near 1.55 μm are especially useful formeasurements, the approach described here may be useful for a widerrange of wavelengths, typically for wavelengths between 0.8 and 4 μm.

It is generally preferred that the film of silicon (or other material)that serves as the absorbing slab 42 is not too thin, because for a verythin film the nature of the surfaces becomes more important, and theseregions may exhibit optical characteristics that differ from those ofthe bulk of the silicon slab. This is especially true when the surfacesare in contact with other materials that may introduce stresses insurface regions. In the SOI structure, such conditions may apply nearthe oxide layer. Forming very thin films of crystalline silicon may alsobe quite difficult in certain circumstances, and thus it may be hard tomaintain consistent results. Another advantage to using relatively thickfilms of silicon is that this makes it easier to wavelength-average overthe oscillations in optical properties that are introduced byinterference effects in the slab. Another advantage of using arelatively thick film is that it allows the film thickness to bedetermined with a very high degree of accuracy, especially if an opticalmethod is used to measure the film thickness, as described below. Yetanother advantage is that a thicker film can be very opaque for shortwavelengths of radiation, especially for wavelengths <˜1 μm. This can bean advantage because the lamp heat sources that heat the wafer typicallyradiate strongly at these short wavelengths. If the silicon film is verythin, the power coupling of the lamps to the wafer may be affected bythe presence of the interface beneath the silicon slab that reflects thelight at the back of the slab. In such cases, the heating cycle of thewafer would be affected, which may be undesirable, especially if itleads to thermal non-uniformity across the surface of the wafer. Typicalthicknesses for the silicon film are in the range between 1 μm and 300μm. For high temperature calibration, the silicon film would normally bemore than 10 μm thick, but less than 100 μm thick. A typical thicknesswould be ˜50 μm.

However, despite the advantages of thicker films in certaincircumstances as discussed above, one of skill in the art will recognizethat in other circumstances thinner films may nonetheless be preferable.

The oxide layer thickness in the SOI structure is typically in the rangebetween 0.001 μm and 100 μm, and it would normally be less than 1 μmthick. The exact thickness can be optimized to make the reflectivity ofthe back surface of the slab as high as possible. A typical value forthe oxide thickness is ˜0.3 μm for a measurement wavelength of 1.55 μm.There can be an advantage in using a relatively thin oxide layer, sincea thin layer has less capability for introducing undesirable thermalstresses in the wafer during heating.

The substrate thickness is mainly determined by mechanical constraints,but for typical applications it should be of a thickness that allows thecombination of the substrate, the oxide layer and the absorbing slab tobe between 200 μm and 2 mm thick. Typically the combination would be 775μm thick, which is the thickness of a standard 300 mm diameter wafer.

The doping of the silicon slab at the surface would usually be selectedso that it is easy to reproduce a known temperature dependence in theabsorption coefficient of the silicon slab. One way to do this is toselect a lightly doped silicon slab. For example, the doping can suchthat the resistivity, p, of the silicon is greater than ˜0.1 Ωcm, andpreferably greater than 1 Ωcm. The doping in the substrate can beselected for convenience. If it is desired that the wafer should be onlyused for high temperature calibration (e.g. at temperatures greater than800° C.), then any normal doping level is acceptable, because thesubstrate will become opaque at high temperatures and there will be noreflection from the back of the wafer to affect the measurements. If theapproach is to be used only at low temperature then it is simpler if thesubstrate is opaque, and a heavily doped wafer with ρ<0.05 Ωcm should beused. For improved opacity in the infra-red wavelength range, ideallyρ<0.02 Ωcm.

If a lightly doped wafer is used, embodiments of the reflectance-basedmethods disclosed herein can be combined with other calibrationmethodologies, including transmission-based temperature calibration,such as those described as in U.S. patent application Ser. No.10/178,950, to yield still further embodiments. In such furtherembodiments, a measurement of transmitted light can be used to determinethe wafer temperature up to the limit set by the fall-off in transmittedlight signal, which is typically ˜850° C. for measurements at awavelength of 1.55 μm. Above this temperature, the reflection-basedapproach can be used. This approach brings several advantages. Firstly,it reduces the number of wafers that need to be used to perform acalibration procedure. Secondly, the temperature deduced from thetransmission measurement can be used to improve the accuracy of thereflection-based measurement. This can be done by ensuring that the twomeasurements agree at a particular temperature. This cross check allowsthe high accuracy of the transmission-based approach to be extended tothe reflection-based approach that has to be used in the hightemperature regime.

The structures utilized for the reflection-based measurement approach donot necessarily need to exist across the entire surface of the wafer.For example, FIG. 18 shows a plan view of a wafer 12 that includes threeregions 80, 80′, and 80″ that have been modified to allow thereflection-based measurement approach to be used. These regions maycoincide with the locations viewed by pyrometers that observe the wafertemperature. The regions may be modified by the formation of the SOIstructure in these regions, and the deployment of coatings, gratings,textured surfaces, sloping surfaces and other features described in thisdisclosure. Multiple measurement sub-systems, each with an associatedset of light sources and optical detectors such as the set suggested inFIG. 1 may be deployed to enable the measurements in each of thelocations where a pyrometer needs to be calibrated. Furthermore,transmission measurements can be performed either in the same location,or at locations near them. There may be situations where it is best toperform the transmission-based measurement at a region where some of thestructures used in the reflection-based approach are not present. Forexample such structures could degrade the quality of thetransmission-based measurements by scattering light. In this case thetransmission-based measurement can still be performed at a location thatis near the point where the reflection-based measurement is performed,and a cross calibration between the two methods, and a correspondingcalibration of the pyrometer can still be performed. For this to bepossible it is best that the lateral separation of the measurementlocations is less than the thermal diffusion length criterion that wasset out in U.S. patent application Ser. No. 10/178,950.

For these methods to be accurate, it is preferable in some embodimentsthat the thickness of the absorbing layers used is known with a highdegree of accuracy. The thickness can then be provided as an input to analgorithm in order to determine the degree of the absorption thatcorresponds to the measured reflectance or transmittance, and hence todeduce the wafer temperature. The algorithm can additionally oralternatively consider other factors, for example, the resistivity, aswell. The thickness, resistivity, and/or other factors may be measuredusing any known method.

For the reflection-based measurement, the thickness of the surface layerof the SOI structure can be determined either during the manufacturingprocess or afterwards. For example, the thickness can be determined bymeasuring a high-resolution reflection spectrum of the wafer in theinfra-red region where the silicon film is transparent. The reflectionspectrum will display oscillations in reflectance that arise frominterference effects within the silicon film, as described above. Themethods of thin film optics can then be combined with knowledge of therefractive index of silicon to obtain a very accurate measurement of thethickness of the silicon layer. In some of the configurations discussedabove, the features introduced in order to reduce the front surfacereflection would also reduce the interference effects. This might makeit more difficult to make the film thickness measurement. In such cases,it may be easier to perform the measurement of silicon thickness at apoint in the manufacturing process before such measures are implemented.

It will be appreciated by one of skill in the art that reflection-basedmeasurements, such as the examples discussed herein, may be used tocreate a temperature uniformity map across the surface of a wafer. Forinstance, several reflectivity measurements could be performedsimultaneously or sequentially in a plurality of different areas acrossthe surface of the wafer. The wafer could include specialized regionsfor ease in separating the measurements, or could be homogenous acrossits surface. Process uniformity could be improved or optimized byobserving such temperature differences.

Difficulties with temperature measurement methods that are based onoptical absorption (α(λ,T)) may arise when the absorption is so strongthat the specimen being used becomes effectively opaque. For example, a300 mm diameter silicon wafer that is typically ˜775 μm thick, transmitsvery little radiation at any wavelength when its temperature exceeds˜900° C. Aspects of certain approaches, such as the earlier-referencedtransmission-based approaches, include the use of very thin siliconwafers, which may comprise one example of a way to address theopaqueness problem. The discussion above can also provide improvementswhere a measurement of reflected radiation is used to provide thetemperature calibration. However, still further improvements may bepreferred in applications where extremely accurate temperaturecalibration is required at high temperatures. Exemplary embodiments ofsuch a method for providing an accurate calibration at high temperaturewill therefore now be addressed.

Such embodiments may share some characteristics with the reflectance-and transmission-based approaches. However, embodiments the presentsubject matter as described below utilize a combination of an opticalabsorption measurement and a measurement that is sensitive to theoptical thickness of a layer. Embodiments of this combination may thusprovide the ability to provide an absolute temperature measurement ofvery high accuracy. One exemplary way to implement the approach isthrough a scheme wherein measurements of wafer characteristics areobtained through the use of beams of light at approximately the samewavelength but with different degrees of temporal coherence.

As well as the above-referenced U.S. patent application Ser. No.10/178,950 and discussion above, there are various methods relating tothe use of measurements of the optical properties to deducetemperatures, especially in the field of semiconductor processing.

As noted earlier, generally a measurement of optical absorption may usedto deduce a wafer temperature. This method has the virtue of providing avery accurate temperature measurement. The method can also provide anabsolute temperature measurement, because the optical absorption at agiven wavelength is uniquely defined at any given temperature in a givenmaterial. It may be implemented by using, for example, reflection ortransmission measurements to deduce the optical absorption. However,since this absorption can be very strong at high temperature, it canbecome difficult to implement, at least when using wafers of standardthickness. The examples described earlier in the present disclosure maybe able to overcome such potential difficulties by using areflection-based approach.

Another possible method of determining temperature is based on ameasurement that is sensitive to the optical path length through asample, which can also be described as an optical thickness. The changein the phase of an electromagnetic wave as it travels through a mediumis related to the product of the real part of the refractive index ofthe medium, n_(m), and the distance traveled, d, which is the opticalpath length, n_(m)d. In a medium where the real part of the refractiveindex is sensitive to temperature, this optical path length through themedium changes as the temperature changes. Furthermore in any materialwith a finite coefficient of thermal expansion, the optical path lengthof a ray that travels between boundaries of the medium will also changewhen the physical dimensions of the material change with temperature.Hence any measurement method that is sensitive to the optical pathlength of a ray of energy passing through the material can be used tosense the temperature of the material. Typically this approach has beenimplemented by measuring the reflectance, R*, or the transmittance, S*of a slab of material, such as slab 50 as shown in FIG. 2. R* and S* arestrongly affected by the interaction between rays of light reflected atthe two boundaries of the slab, as a result of interference effects. Theinterference phenomenon arises because of the wave nature of the light,and it depends on the relative phase of waves that are reflected at thetwo surfaces of the slab. Since the relative phase of waves reflected atthe two surfaces of a slab is determined by the difference in theoptical path lengths traversed by these rays it is strongly affected bytemperature.

One of skill in the art will recognize that an optical-path-length-basedapproach generally requires that the light that is detected in themeasurement acts in a coherent manner, since the phenomenon ofinterference hinges on the relationship between the phases of the wavesthat are reflected at two interfaces. The phase relationship is onlywell defined in the case where the waves act in a temporally coherentmanner. In practice this means that for a medium that is reasonablythick, such as a standard silicon wafer that is ˜775 μm thick, themeasurement must be carried out using a coherent light source such as alaser, which emits a very narrow range of wavelengths. The light can betreated as being coherent if the wavelength range of the light that ismeasured, Δλ, is small enough. One criterion is that

$\begin{matrix}{{{\Delta\lambda}{\operatorname{<<}\frac{\lambda^{2}}{4n_{m}d_{m}}}},} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$where n_(m) is the refractive index of the medium that makes up theslab, and dm is its thickness. For a wafer that is 775 μm thick,considering the wavelength of 1.55 μm and assuming that n_(m)corresponds to that for silicon and is ˜3.6, Eq. 6 indicates that Δλneeds to be much smaller than 0.2 nm in order for the light to betreated as being coherent. For a thinner film, the requirement is lessstringent. For example, for the same conditions but with a thin film ofsilicon that is 10 μm thick, then Δλ need only be much smaller than 16nm. Optical-path-length-based measurements can also be performed with arelatively incoherent source of radiation, which emits a wider range ofwavelengths, provided that the optical detection system includes afilter that only allows a very narrow range of wavelengths to contributeto the detected signal. In this case the filter bandwidth would have tobe limited to a range similar to Δλ. This approach is practical forreasonably thin films, such as the 10 μm-thick silicon film discussedabove, but may become very difficult to use if the distance between thesurfaces of the slab is large, because the requirement for an extremelynarrow-band filter prevents most of the energy from reaching thedetector and leads to an impractically low signal level.

This discussion illustrates an important concept regarding the opticalcharacteristics of the radiation that is sensed in the measurementsdiscussed in this disclosure. The concept is that of the coherencelength of the radiation. The coherence length, d_(coh), describes themaximum interval along a ray of light traveling in a medium withrefractive index n_(m) where the phase of the electromagnetic wave atthe beginning of the interval maintains a fixed relationship to that atthe end of the interval, as prescribed by the wave equation. For aninterval along a ray that is significantly longer than the coherencelength these is no predictable relationship between the phases of thewave at the two ends of the interval. The coherence length is typicallycharacterized by the definition

$\begin{matrix}{{d_{coh} = \frac{\lambda^{2}}{n_{m}{\Delta\lambda}}},} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$where the symbols take the meanings discussed above. This criterion isclosely related to that given in equation (6). Radiation with acoherence length that is long relative to the path length through a slabcan be easily used to observe interference effects in that slab, whereasmeasurements based on the observation of radiation with a coherencelength that is short relative to the path length through the slab willnot demonstrate such effects. In this disclosure the term coherent isused generally when discussing situations where the rays of radiationpassing through a medium interact in a manner where they maintain awell-defined phase relationship, and the term incoherent when L thatcriterion does not apply. Likewise a “coherent measurement” is one thatrelies on the detected radiation acting in a coherent manner and an“incoherent measurement” is one that relies on the detected radiationacting in an incoherent manner.

One advantage of temperature measurement approaches based on opticalpath length measurements is that they can be extremely sensitive totemperature, especially when the physical path length through thesemiconductor wafer is relatively large. However there are severalpotential difficulties with the approach. The first problem is that itis oftentimes extremely difficult to use the approach to determine theabsolute temperature of the wafer. This is because the reflectance andtransmittance tend to be periodic functions of temperature, and henceany particular reflectance or transmittance value could correspond tomany different temperatures. A second problem is that the reflectanceand transmittance are also extremely sensitive to both the thickness ofthe layer and its refractive index. Hence, in order to characterize theabsolute temperature dependence of the optical properties of a givenslab it is generally necessary to determine both these quantities withan extraordinary degree of absolute accuracy. In principle, for anygiven slab of material, such problems could be overcome bycharacterizing the reflectance and transmittance of that particular slabas a function of absolute temperature, but this would make for a rathercumbersome approach in practical applications. Furthermore, it would notresolve other issues, such as the fact that the reflectance andtransmittance are also very strongly affected by the angle of incidenceof the radiation, largely because this directly affects the optical pathlength through the layer. In practice most temperature measurementschemes that have been proposed based on the effect of a changingoptical path length have been used to measure changes in temperature.This can cause problems when tracking the temperature of a wafer duringa semiconductor processing step, if the initial temperature of the waferis not known accurately. A final problem, which will also be addressedbelow is that, at least in semiconductor materials, optical absorptionrises rapidly at high temperatures, and eventually the ray that passesthrough the layer is so strongly attenuated that it no longer produces asignificant effect on the reflectance or transmittance. The latterproblem mirrors the difficulty in using transmission measurements athigh temperatures that was mentioned earlier.

Embodiments of the method of the present subject matter include those inwhich at least one of the materials in the wafer whose temperature is tobe determined has the characteristic that its optical absorption at aknown wavelength varies with temperature, and those in which at leastone of the materials has the characteristic that its optical thicknessat a known wavelength varies with temperature. The two wavelengthsmentioned can be the same, but this is not essential. The two materialscan also be same, but this is also not essential. The method relies onusing a measurement of the absorption characteristic to determine anabsolute temperature value. It also relies on using the temperaturevariation of the optical thickness to determine a change in temperature.The combination of the accurate measurement of the absolute temperatureand the accurate measurement of the temperature change enables thecreation of an accurate temperature scale covering a wide range oftemperatures.

The approach can be used for a single slab, such as that shown in FIG.19( a), in the case where the slab contains a material whose opticalabsorption at a wavelength varies with temperature and whose opticalthickness varies with temperature.

FIG. 19( b) shows another example of a structure that can be used toperform the calibration. The structure has two layers. One of the layerscan provide the temperature-dependent absorption and the other canprovide the temperature-dependent optical thickness.

Other embodiments (not shown in FIG. 19) include multilayer structuresin which one layer provides a temperature-dependent optical thicknessand a combination of that layer with another layer (or layers) providean optical absorption that varies with temperature, or vice-versa.Additionally, it will be appreciated that, for example, various or allthe layers shown in FIG. 19 could be implemented using multilayerstructures.

The structure used in the calibration procedure can also take morecomplex forms, such as the example shown in FIG. 19( c). In this case,an extra layer is included. The extra layer can be used to generate areflected wave. This configuration may be useful, for example, in caseswhere the surface layer and the substrate are materials with verysimilar optical properties and hence where there would not normally be astrong reflection at their interface.

For an example of how the measurements can be performed, attention isbriefly directed again to FIG. 1. As noted above, FIG. 1 illustrates anexemplary RTP process chamber 10, where the wafer 12 is heated by banksof lamps 14 and 16. In the example shown the banks of lamps are bothabove and below the wafer. The chamber 10 further includes at least onelight source 30, and can include various sensors such as thoseillustrated at 32, 34, 38, 38, and 40, or in other suitableconfigurations.

FIG. 20 shows aspects of an exemplary embodiment of the measurementapproach in more detail, in this case illustrated for a wafer 100 takingthe form in FIG. 19( a). It should be noted that the wafer may also havesurface coatings or patterns on either or both of its surfaces, althoughthese are not shown in the figure. The figure shows a ray from a source110, which emits radiation AINC that is incoherent. This radiation canbe used to determine the degree of absorption in the substrate 100,either by means of a reflection measurement using RINC or a transmissionmeasurement using TINC. Appropriate signals for such measurements arecollected by the detectors 112 (collecting reflected incoherent energyRINC) and 114 (collecting transmitted incoherent energy TINC). Theapparatus also has a source 120 which emits radiation ACOH that iscoherent. This radiation can be used to determine a change in theoptical path length through the wafer. For example, the path length mayaffect the reflectance or transmittance of the wafer. Appropriatesignals for measurement of these quantities are collected by thedetectors 122 (collecting reflected coherent energy RCOH) and 124(collecting transmitted coherent energy TCOH). In some cases, the source110 may be the same source as 120. In such a case, the wavelength rangedetected by the detectors used for reflectance or transmittancemeasurements can be adjusted to a condition suitable for measurements ofcoherent or incoherent light. Such adjustment is possible by selectingan appropriate optical bandwidth for the filters in front of thedetectors. For the coherent radiation measurement a narrow band filterwould be used, whereas for the incoherent radiation measurement a widerband filter would be used. Hence it is possible that the detector 112could also serve as the detector 122, and the detector 114 could alsoserve as the detector 124.

FIG. 21 shows another exemplary optical configuration, where the energyfrom the two sources 110 and 120 passes through a common optical path130 before illuminating the wafer, and also passes through commonoptical paths when it enters detection systems 132 and 134. In thiscase, the coherent and incoherent measurements can be performed with asimpler apparatus, even if the wavelength ranges of the sources 110 and120 overlap. The optical filters in front of the detectors in 132 and134 preferably have bandwidths that are sufficiently wide to allow bothwavelength ranges to reach the detectors. One way of implementing thisapproach, yet still allowing for separately performing the coherent andincoherent measurements, is by modulating the output of the two sourcesof radiation with two different signals. In this case, the contributionsof the light from the two sources can be distinguished even if bothbeams of light are sampled by just one detector. For example, the outputof the source 110 can be modulated with a periodic signal from amodulator 108 with a frequency f_(inc), and that of the source 120 canbe modulated with a periodic signal from a modulator 118 with frequencyf_(coh). Various forms of modulation can be employed to produce lightfrom either or both sources that varies in time. For example, sinusoidalmodulation or a square-wave modulation may be employed. The two signalscan be separated by coupling the output of the detectors to two lock-inamplifiers which selectively measure frequency components at thefrequencies f_(inc) and f_(coh). For example, the output from thedetector of reflected light 132 can be provided to the input of twolock-in amplifiers, 128 (AMPR:f_(coh)) and 118 (AMPR:f_(inc)). In thiscase, the lock-in amplifier AMPR:f_(coh) is tuned to the frequencyf_(coh) and hence extracts the signal from the coherent light reflectedfrom the wafer. The lock-in amplifier AMPR:f_(inc) is tuned to thefrequency f_(inc) and hence extracts the signal from the incoherentlight reflected from the wafer. Likewise, the output from the detectorof transmitted light 134 can be provided to the input of two lock-inamplifiers, 127 (AMPT:f_(coh)) and 117 (AMPT:f_(inc)). In this case thelock-in amplifier AMPT:f_(coh) is tuned to the frequency f_(coh) andhence extracts the signal from the coherent light transmitted by thewafer. The lock-in amplifier AMPT:f_(inc) is tuned to the frequencyf_(inc) and hence extracts the signal from the incoherent lighttransmitted by the wafer.

The exemplary scheme in FIG. 21 presents may advantageously reduce thenumber of light detectors and optical filters that need to be used toperform the measurements. It is also a convenient way of using a commonset of optics for coupling light into and out of the chamber, and forensuring that the two types of optical measurement (coherent andincoherent) are performed at the same location on the wafer surface.This latter point is especially powerful if the measurements areperformed at similar wavelengths. This is because most opticalcomponents, such as lenses, display chromatic aberrations, which meansthat their focusing properties vary with wavelength. As a result, whenlight of multiple wavelengths is coupled through an optical system, thesize, shape and locations of focused regions of light may vary dependingon the wavelength. Such problems can be decreased by the use ofsophisticated optical designs, or through the use of reflective optics,but these approaches are typically more complicated and may beexpensive.

In contrast, the method described here can use light at similarwavelengths to perform the two types of measurement, so that themeasurements are performed in practically identical locations on thewafer, with practically identical size and shape of the probed region.In one example, the source 120 can be a semiconductor laser that emitslight containing a range of wavelengths less than ˜1 nm, centered on awavelength of 1550 nm. For high-coherence measurements, the wavelengthrange should be even smaller, e.g. <0.5 nm. Such a source can have acoherence length greater than the thickness of the optical slab, andhence can be effectively used to monitor changes in the opticalthickness of the slab. The source 110 can be a light-emitting diode,which emits light containing a range of wavelengths greater than 2 mm,also centered on a wavelength around 1550 nm. For highly incoherentmeasurements, the wavelength range should be even greater, e.g. >5 nm.Such a source can have a coherence length much smaller than thethickness of the optical slab, and hence can be effectively used tomonitor changes in the optical absorption of the slab. Both sources canbe conveniently modulated by electrical signals. The detectors 132 and134 can be photodetectors, such as InGaAs photodiodes.

Although in the last example the two sources were centered in the samewavelength region, the principles of the approaches described here maystill be applied when there is the centre wavelengths are different. Insome cases, it may be preferred to use two wavelengths where theabsorbing layer in the wafer exhibits significant differences in opticalabsorption at the two wavelengths. For example, it may be preferablethat the absorption is relatively high for the purposes of accuratelymeasuring the degree of absorption in the absorbing layer, yetsimultaneously preferable for the absorption to be relatively low at thewavelength used to track the changes in the optical thickness of thelayer. In such a case, two different wavelengths may be selected thatmeet these two criteria. For example, when applying the approach with astructure such as that in FIG. 19( a), e.g. a silicon wafer that is ˜775μm thick, it could be convenient to use a wavelength ˜1050 nm todetermine the absolute temperature of the wafer when it is around ˜100°C., and then to use a high-coherence light source with a wavelength˜1550 nm to track the change in wafer temperature as the wafer isheated. When wavelengths that are very different are used, it may becomemore desirable to use the approach shown in FIG. 20, with separate lightsources and detectors. In some embodiments, the optics can be arrangedso that the regions sampled on the wafer can be very close together ifnecessary. This may be useful, in order to reduce errors in thetemperature calibration.

An alternative approach is to ensure that wafer is rotating, and to makemeasurements at the same radius on the wafer. Another approach is to usejust one set of detection optics, but to provide a filter with a tunableband-pass in front of the detectors. Various such filters are available,such as monochromators and other devices that can scan through aspectrum of light, variable wavelength filters, switched filters etc.The detection system can also include multiple detectors combined withseparate filters or a spectrally dispersive element, such as a gratingor a prism, which separate the wavelength components in the light andguide them to different detectors. It will be appreciated that variousembodiments may also utilize a filter that passes both wavelengthcomponents while rejecting stray light, for example.

When the wafer that is being heated can be specially selected, forexample, to serve as a temperature calibration standard, it is possibleto use one wavelength region for both measurements of absorption andoptical thickness, but to employ a composite wafer structure, where alayer that is used for the optical thickness measurement is relativelytransparent at a given wavelength and a second layer that is used forthe optical absorption measurement is relatively absorbing at the samewavelength. Such structures can take the forms suggested in FIGS. 19( b)and 19(c). In other embodiments, the layer used for one of themeasurements can actually include the second layer. For example, a waferin accordance with FIG. 19( c), may comprise a structure where the layerwith temperature dependent optical absorption is a silicon substratethat has a substrate thickness d_(sisub)˜750 μm thick, and which isrelatively lightly-doped, for example with a resistivity >0.5 Ωcm. Thelayer with temperature dependent optical thickness can also be lightlydoped silicon, with a similar resistivity, but it could be thinner, witha surface layer thickness d_(sisurf)˜25 μm thick. The separation layerbetween the two silicon layers can be a layer of silicon dioxide, whichensures that light can be reflected from the lower surface of the uppersilicon layer. The silicon dioxide layer could be ˜0.3 μm thick. In thisstructure, the optical absorption in the silicon can be probed by makinga transmittance measurement. Now, in this case, since both siliconlayers have very similar optical properties, both layers havetemperature dependent absorption. Hence, this is an example the layerwith temperature dependent absorption could be considered as being theentire wafer thickness, including both silicon films. Indeed, theoptical thickness of both silicon layers is also a function oftemperature. However, at high temperatures (e.g. >850° C.), very littleof the light reflected at the back surface of the thicker, lower siliconlayer can return to the upper surface of the wafer and hence it cannoteffectively contribute to an interference effect between light reflectedat the two outer surfaces of the wafer. On the other hand, light that isreflected at the back surface of the upper silicon layer (at theinterface with the silicon dioxide) can return to the surface andinterfere with that reflected at the upper surface of the upper siliconlayer. Hence, an optical thickness measurement can be convenientlyperformed on the upper silicon film. This allows temperaturemeasurements to be extended to temperatures above 850° C. It isconvenient for the wavelength to be around 1550 nm, since the absorptionin silicon is relatively low at this wavelength. Indeed, with thisstructure, it may be preferred to perform all the measurements usingjust a single light source. This is because the transmittancemeasurement that is used to deduce the absolute temperature of the wafercan be conducted at a temperature that is high enough for theinterference effects to be negligible. That condition arises when verylittle of the light that is reflected from the back surface of the wafergets back to the front surface of the wafer, because optical absorptionis too strong. The condition is met at a temperature T_(op) when theproduct of the optical absorption coefficient α(λ_(S),T_(op)) at thewavelength used for the transmission measurement, λ_(S), and thecombined thicknesses of the silicon films,d_(sicomb)=d_(sisurf)+d_(sisub), is greater than ˜3. In this case thefraction of the energy in a ray that is left after it passes through thethickness of the wafer is ˜exp(−α(λ_(S),T)d_(sicomb))=exp(−3)<5%. Ifλ_(S) is ˜1550 nm, then at ˜800° C. α(λ_(S),T) is ˜100 cm⁻¹. For a casewhere d_(sicomb) is ˜775 μm thick, α(λ_(S),800° C.)d_(sicomb) is ˜7.8,and the criterion is easily met. However, the surface layer is stillrelatively transparent, because λ(λ_(S),800° C.)d_(sisurf) is only˜0.25. Hence, in this case the transmittance measurements and theoptical thickness measurements can both be performed with a coherentlight source emitting light at a wavelength ˜1550 nm. Although theillustration emphasizes the relative simplicity of such a scheme interms of the number of components that are utilized, it also serves toshow that the methods can be carried out using coherent light sourcesalone, if desired.

In principle, it is also possible to use just the coherent source toimplement the method even when the interference effects are significantin transmittance or reflectance measurements. However, in this case, theoptical absorption would be deduced from a more sophisticated analysisof the reflectance and transmittance signals, which takes into accountthe way that absorption attenuates the degree of interference observedbetween light reflected at two interfaces in the wafer. By deducing thedegree of absorption, the absolute temperature can be established, withthe interference being used to determine change(s) in temperaturerelative to the absolute temperature.

FIGS. 22 and 23 are flow diagrams giving examples of how the temperatureof the wafer at a process temperature can be determined with a highdegree of accuracy.

Turning to FIG. 22, a first measurement would typically be performed ona wafer that has been loaded into the process chamber as shown at step150, either before the heating has started, or at a point relativelyearly in the heating cycle, at least at a temperature below theprocessing temperature that needs the tightest degree of temperaturecontrol. In this example, at step 152 the optical absorption in thewafer at a probe wavelength is determined at a first temperature, T₁.The optical absorption can be determined by means of a transmittancemeasurement or a reflectance measurement. Such measurements can be usedto determine the optical absorption by a variety of methods, including,but not limited to, those described and discussed above in the presentdisclosure, and/or other methods, such as, for example, those discussedin U.S. patent application Ser. No. 10/178,950. Once the opticalabsorption has been determined, at step 156 the absolute temperature ofthe wafer, T₁, is established from the optical absorption with highaccuracy. Such measurements are relatively easy to perform even onwafers that are quite thick, such as typical wafers used in devicemanufacturing, provided that T₁ is low enough for an acceptable amountof light to reach the back surface of the slab. This approach providesan initial measurement of the wafer temperature T₁.

Next, at step 158, a measurement affected by the optical thickness of atleast some part of the wafer is performed. This measurement of anoptical property of the wafer is preferably performed using a coherentmeasurement approach. The optical property would typically be thereflectance or the transmittance of the wafer, but the basic requirementis that the optical property that is measured is affected by an opticalpath length through a structure in the wafer. This optical path lengthis a function of wafer temperature, typically because of the effect oftemperature on either the refractive index or the physical dimensions ofat least part of the wafer. Once the optical property has been measured,the wafer temperature is changed at step 160 to a second temperature,T₂. At step 162, the coherent measurement is repeated, and the change inthe optical property is determined at step 164. The change in theoptical property is used at step 166 to deduce the temperature changethat has occurred, ΔT, as the wafer temperature changed from T₁ to T₂.This change can be deduced with great accuracy, because of the strongeffect of optical path length changes on coherent measurements. Finally,an accurate absolute value for T₂ is obtained by adding ΔT to T₁ at step168.

Coherent measurements of optical path length have sometimes beenproblematic with regard to sensing the sense of a temperature change(i.e whether temperature is rising or falling). This is because suchmeasurements give rise to changes in optical properties that are highlyoscillatory. If the wafer temperature changes at a point thatcorresponds to a maximum or a minimum in the oscillatory signal, then itcan be difficult to tell whether the wafer is heating or cooling.Various approaches have been suggested for overcoming this problem,including the use of multiple wavelength measurements and examining theeffects of wafer thickness variations on the interference effects.However, in embodiments of the present subject matter, such problems maybe alleviated by ensuring that the optical absorption is estimated,either from a second measurement, or by analyzing the coherentmeasurement and deducing an absorption value. By sensing the change inabsorption it is possible to get an immediate check on the sense of thetemperature change, and hence the problem is resolved.

For example, the flow chart of FIG. 23 shows how the approach of FIG. 22been adapted to perform a second measurement of absorption at thetemperature T₂ at step 170 following step 166. The steps 150-166 mayremain the same as in FIG. 22. The absorption measurement at step 170can then be used to validate the direction of the temperature changefrom T₁ to T₂ by estimating the value for T₂ at step 172 using theabsorption measurement. Using the temperature estimate and/or theabsorption measurement, at step 174 a sense of the direction of ΔT (i.e.rising or falling) can be determined. For example, when the absorptionmeasurement is performed using a silicon layer, any increase inabsorption always corresponds to a rise in temperature. Therefore, insuch cases, if the absorption at T₂ is greater than that at T₁, then thetemperature has risen. Using that information, at step 176, thetemperature T₂ may be deduced by adding or subtracting ΔT asappropriate. Although it may be difficult to perform the absorptionmeasurement (for example when signal levels are very low due to verystrong absorption at high temperature), an accurate value is notnecessary for the purpose sensing the direction of the temperaturechange. The estimate need only be accurate enough so that it can bedetermined whether the temperature is rising or falling. Additionally,the wavelength of radiation used to sense absorption can be selected tofacilitate that task; it need not be the same as the wavelength used todetermine the optical path length changes.

The approaches for determining temperature changes can be repeated andhence the temperature of a wafer can be tracked throughout a heatingcycle. This can be done with an initial cross-calibration to an absolutetemperature measurement, for example, through the optical absorptionmeasurement. It can also be done with periodic cross-checks againstmeasurements based on optical absorption, which can also be used toconfirm the sense of the temperature changes. In many processes, thedifficulties with the sense of temperature changes can be eliminated,because it is possible to monitor the heating power applied to the wafer(and any other factors that could impact heat transfer, such as thenature of any gas flows that could transfer heat to or from the wafer)and hence predict the sense of the temperature change. In particular, ina heating cycle where the measurements are performed in order tocalibrate another temperature sensor, such as a pyrometer, there isextra flexibility. For example, the heating system may be programmed todeliver a continuously rising output of heating power to a wafer thatstarts at a temperature that is below that of the processingenvironment. In this case it is known that the wafer temperature will becontinuously rising in response to the heating power. Likewise if theheating power is shut off, the wafer will start to cool (although careshould be taken to ensure that the thermal time-constants of components,such as heating lamps, are taken into consideration). Measurementsperformed during the cooling curve can then be based on the assumptionthat the wafer temperature is decreasing. Indeed, the cooling trendcould also be confirmed by other means, even by using the uncalibratedoutput of a pyrometer, since the signal strength of radiation thermallyemitted by the wafer decreases with the temperature of the wafer.

It is appreciated by persons skilled in the art that the presentlydisclosed subject matter is not limited in scope by what has beenparticularly shown and described above, which constitute variousexamples. Rather, as set forth in the attached claims, the scopeincludes both combinations and sub-combinations of various featuresdiscussed herein, along with such variations and modifications as wouldoccur to a person of skill in the art.

1. A method of calibrating a temperature measurement device, the methodcomprising: directing light towards a first side of a calibration wafer,at least part of the calibration wafer having an optical absorption at afirst known wavelength that varies with temperature and having anoptical path length at a second known wavelength that varies withtemperature; heating the calibration wafer; measuring an absorptioncharacteristic of the calibration wafer at the first known wavelength todetermine an absolute temperature value; making at least a firstmeasurement and a second measurement of a value of an optical propertythat is sensitive to the optical path length of the light being directedthrough at least part of the calibration wafer, wherein the firstmeasurement and the second measurement are performed at differenttemperatures of the calibration wafer; determining a change intemperature based upon the measured values that are sensitive to theoptical path length through at least part of the calibration wafer; andcalibrating a temperature measurement device by correlating readings ofthe temperature measurement device with both the measurement of theabsolute temperature value and the measurement of the change intemperature.
 2. A method as defined in claim 1, wherein the calibrationwafer comprises only a single slab of material.
 3. A method as definedin claim 1, wherein the calibration wafer has two layers.
 4. A method asdefined in claim 1, wherein the absorption characteristic at the firstknown wavelength and the variation of the optical path length at thesecond known wavelength are measured by detecting light transmittedthrough the calibration wafer at the respective wavelengths.
 5. A methodas defined in claim 1, wherein at least some of the light that isdirected towards the first side of the calibration wafer is emitted byan incoherent light source.
 6. A method as defined in claim 1, whereinthe calibration wafer comprises silicon.
 7. A method as defined in claim1, wherein the temperature measurement device comprises a pyrometer. 8.A method as defined in claim 1, wherein the second known wavelength isabout 1.55 microns.
 9. A method as defined in claim 1, wherein at leastsome of the light that is directed towards the first side of thecalibration wafer is emitted by a coherent light source.
 10. A method asdefined in claim 1, wherein the light that is directed towards the firstside of the calibration wafer comprises light emitted by an incoherentlight source at the first known wavelength and light emitted by acoherent light source at the second known wavelength.
 11. A method asdefined in claim 1, wherein the measurement of the absolute temperaturevalue and the measurement of the change in temperature are conductedwhile the calibration wafer is rotating and wherein both measurementsare taken at the same radius on the calibration wafer.
 12. A method asdefined in claim 1, wherein a temperature scale is created based on boththe measurement of the absolute temperature and the measurement of thechange in temperature, the temperature scale being used to calibrate thetemperature measurement device.
 13. A method of calibrating atemperature measurement device, the method comprising: measuringtransmission through a calibration wafer at a first wavelength todetermine at least one absolute temperature of the wafer as the wafer isheated; measuring transmission through the calibration wafer at a secondwavelength to determine at least one change in temperature of the waferas the wafer is heated, the second wavelength being selected such thatoscillations occur between maxima and minima in reflectance ortransmittance of the wafer as the temperature of the wafer increases;and calibrating a temperature measurement device by combining thedetermined absolute temperature with the determined change intemperature of the wafer.
 14. A method as defined in claim 13, whereinthe calibration wafer comprises only a single slab of material.
 15. Amethod as defined in claim 13, wherein the calibration wafer has twolayers.
 16. A method as defined in claim 13, further comprising the stepof directing light towards a first side of the calibration wafer at thefirst wavelength and at the second wavelength, the light being directedtowards the first side of the calibration wafer at the first wavelengthbeing emitted by an incoherent light source and wherein light that isdirected towards the first side of the calibration wafer at the secondwavelength is emitted by a coherent light source.
 17. A method asdefined in claim 13, wherein the calibration wafer comprises silicon.18. A method as defined in claim 13, wherein the temperature measurementdevice comprises a pyrometer.
 19. A method as defined in claim 13,wherein the second known wavelength is about 1.55 microns.
 20. A methodas defined in claim 13, wherein the measurement of the absolutetemperatures and the measurement of the changes in temperature areconducted while the calibration wafer is rotating and wherein bothmeasurements are taken at the same radius on the calibration wafer. 21.A method as defined in claim 13, wherein the calibration wafer has acomposition that is known ahead of the calibration process so that theoptical properties of the wafer are known.
 22. A method as defined inclaim 13, wherein the transmission measurements at the second wavelengthare sensitive to an optical path length of light at the secondwavelength through the wafer.
 23. A method as defined in claim 13,wherein determined absolute temperatures at the first wavelength arebased upon an optical absorption of the wafer at the first wavelength.24. A method as defined in claim 13, wherein the first wavelength andthe second wavelength are the same.
 25. A method as defined in claim 13,wherein a plurality of changes in temperature of the wafer aredetermined at the second wavelength.
 26. A method as defined in claim25, wherein a temperature scale is created for the calibration wafer bycombining the determined absolute temperature with the determinedchanges in temperature of the wafer and the temperature scale is used tocalibrate the temperature measurement device.